[Nevadaref]

BITS, That is decent try. I don't agree with it, but I do appreciate time and effort you put forth. Now I have to accept the intellectual challenge and demonstrate why it is not as you argue.

I will go through your post point-by-point as JR did (although I believe that he failed to grasp your main one), but first I must state that your contention that the ball cannot become live due to the Trail holding his hand in the air fails miserably in the NCAA womens game. Afterall, that's the approved mechanic for chopping in the clock when the Lead administers a throw-in!
Now to your post which I will argue solely with NFHS rules and mechanics.

Originally Posted by Back In The Saddle

It is certainly true that 6-1-2-b says “The ball becomes live when: On a throw-in, it is at the disposal of the thrower.” That sounds pretty authoritative, pretty absolute. It sounds that way because the rules committee opted not to complicate 6-1-2 with details about when it isn't true. But they did attach the following note directly to 6-1-2: "Any rules statement is made on the assumption that no infraction is involved unless mentioned or implied. If such infraction occurs, the rule governing it is followed. For example, a game or extra period will not start with a jump ball if a foul occurs before the ball becomes live." So we need to consider that there are circumstances where some other rule takes precedence over 6-1-2.

Yep, so we are looking for something that would tell us that the Trail desire that play not restart takes precedence over the Lead's desire and action to restart it or vice versa.

Originally Posted by Back In The Saddle

5-8-2-c & d say: "Time-out occurs and the clock, if running, shall be stopped when an official: ...Stops play: ...Because of unusual delay in getting a dead ball live." or "...For any other situations or any emergency." Whether you consider stopping play to bring in subs to be an "unusual delay" or just "any other situation," the official is clearly permitted to do it, and by doing so has caused time-out.

I don't consider this part to be relevant. The clock is already stopped during the situation at hand and we know that time is out. What we are debating is whether time continues to be out or not. So let's move on.

Originally Posted by Back In The Saddle

Now you may certainly argue that while the T did stop play, the L subsequently started it again by giving the thrower the ball.

We have no idea who originally stopped the play. The OP didn't tell us. The Trail did desire to prevent play from restarting and the Lead equally desired it to restart. Who carries more weight in that situation is the debate.

Originally Posted by Back In The Saddle

But 5-9-1 says: "After time has been out, the clock shall be started when the official signals time-in. If the official neglects to signal, the timer is authorized to start the clock as per rule, unless an official specifically signals continued time-out."

But aren't both officials signalling continued time-out during this action? The Lead is handing the ball to the thrower and holding his hand up. The Trail is standing there watching and also holding his hand up. The timer should be doing nothing, but watching. As far as he knows both officials are happy with the action taking place. There has not been any signal to the contrary. Well perhaps there is. In NFHS, the Trail should not have his hand up, but what timer knows that? Heck, if his partner doesn't think anything is wrong, why should the timer? We shouldn't be playing, but we are! So what carries the day de jure or de facto? Most frequently de facto wins that case.

Originally Posted by Back In The Saddle

How does an official stop play and cause time-out to occur? By putting his hand up and blowing his whistle. How does an official signal continued time-out? By keeping his hand up. Does continued time-out indicate a dead ball, of course it does.

Agreed and we do have one official attempting to do that. His partner is ignoring him though.

Originally Posted by Back In The Saddle

The argument was made that since the T didn't sound his whistle to stop the throw-in, the ball became live and the subsequent play must stand. However, "The official's whistle seldom causes the ball to become dead (it is already dead)." Since the ball cannot be live during continued time-out, and our intrepid T was signaling continued time-out, "it is already dead", lack of whistle not withstanding.

I don't agree with that. Every throw-in has the ball become live during continued time-out. You are trying to say that the Trail is signalling a continued dead ball. Symantics really, so let's grant you that part. The problem is that we have the other official taking action to make the ball live. So now it is A vs B and we still don't have any reason to pick one over the other. Your best argument is to say that A signalled first! We'll have to come back to that.

Originally Posted by Back In The Saddle

Also, consider the equal authority clause: “No official has the authority to set aside or question decisions made by the other official(s)” there is at least one notable exception, the timer’s decision to start the clock “as per rule” is specifically set aside by the official’s decision to signal continued time-out.

The equal authority clause applies to game officials on the court, not to the table crew. Therefore, what you are trying to say by this doesn't follow logically. This is a battle between the Trail and Lead on the floor. The timer is not part of it.

Originally Posted by Back In The Saddle

And if the clock cannot start, how can we sensibly argue that the ball should be live anyway? To do so would force the thrower into a nonsensical paradox: The ball becomes live when handed to the thrower, but the clock cannot start even if the thrower passes the ball inbounds. The only thing he can do successfully is violate. Such an argument also ignores 6-1-2-Note.

You are assuming the conclusion before proving it is true. Why can't the clock start? Because the Trail has his hand up, but you have yet to demonstrate why that takes precedence over the Lead administering the throw-in and starting play. If the throw-in had been completed, the Lead would certainly chop in time and might well even start a closely guarded count. If the play was at the other end of the floor and the administering official was the Trail, he would certainly start a 10 second backcourt count. So if the timer is watching that official, the clock is going to start. At best the timer is going to see the two officials doing different things and be confused as to what to do.
Here is where you can point to 5-9-1 and argue that an official is specifically signalling continued time-out. However, we can't dispense with the first part of that sentence. "If the official neglects to signal, the timer is authorized to start the clock as per rule, unless an official specifically signals continued time-out." The covering official hasn't neglected to signal in our play because the ball has not yet been touched inbounds, so this sentence isn't relevant for our specific play. Yet I will even continue further and allow for the case in which the throw-in is completed, since that is what you are basing your paradox upon. If that does happen, is the Lead going to neglect to signal? I doubt it. So again this rule is not applicable. We have one official signalling time in and another signalling continued time out. Still no decision on who takes priority. Again I believe that the best you can do is say that the continued time-out signal came first and therefore should have priority. I'll counter that later.

Originally Posted by Back In The Saddle

So, when an official is signaling continued time-out, and his partner erroneously puts the ball at the disposal of the thrower, that official has very solid backing to rule that the ball never became live and any subsequent action (except perhaps intentional and flagrant fouls) should be ignored.

First, I don't concur that you have proven your case. It is at best indeterminate so far. Second, I don't agree that an official signalling or stating that the ball will remain or become dead necessarily makes it so. The same for it becoming live. That's a rather confusing statement, so allow me to elaborate. I went through the case book seeking plays in which the ball was supposed to be of one status (live or dead), but it became the other. I was especially looking for case plays in which the real game action was consequently nullified or could not be nullified.