3.6 not 2.8 secs left and bad stuff happens

[Nevadaref]

I went and watched a good friend of mine work a GV game last week. It turned out to be one heck of contest. White misses two FTs with the score tied and 7.8 seconds on the clock. There is a scramble for the ball and Green comes up with it, but the player is on one knee and surrounded. She smartly requests a time-out. This is granted with 3.6 seconds remaining.
Following the time-out Green will inbound from a designated spot on the endline at White's basket on the tableside. The R is administering the throw-in. The inbounder throws a long, diagonal pass that is knocked immediately OOB about seven feet past the divison line on the opposite side of the court from the table by her teammate. The player who hit the ball and the defender were right up against the sideline and knocked the ball straight down and OOB directly in front of the C, who was my friend and he immediately hit the whistle and made the call. Since White will now be getting the ball they request a time-out. I look at the clock and it still shows 3.6 seconds. I know for certain that the clock did not move because I wrote down the times of all of the time-outs during the game. That is something that I always do when I observe games.
The timer hit the horn and the R went over the the table said something and then left.
Now, my friend, the U2, goes over to the R, still during the time-out, and has a little conversation. He later told me that he told him that the clock never started, and that it should have because the ball was definitely touched, otherwise they would be inbounding down on the endline. He asked the R if he wanted to do anything about the clock. The R said that he was just going to leave it where it was.
In my postgame talk with my friend, we discussed that no one had count and it would be difficult to ascertain such a short amount of time anyway, perhaps 3/10ths of a second. Therefore, I told him that, according to the rules, in the absence of definite knowledge the clock has to be left as is even though it looks bad. The timer just made a small error.
Of course, my friend is now the Trail opposite table for the critical last possession. The ball is inbounded to a guard who drives the ball up court to the foul line and dishes to a post player on the block. She catches spins and tosses one up AT THE BUZZER. Naturally, the ball bounces on the ring a bit and falls in. My friend counted the basket and the home team won by two.
I happened to be sitting about twenty feet away from the shooter on that side of the court, and I thought that the shot was just a hair late. It was so darn close though. Calling it good was certainly NOT obviously wrong.
Anyway, after the final two league games on Friday and Saturday, the team that won this game ended the season tied for the final playoff berth with another school. This team won the head-to-head tiebreaker. So this whole sequence did have significant meaning.
Now, I'm not relating this story to knock my friend (He is great official and will work a regional final and at the state tournament this year.), but I am looking for feedback on how some of you would have handled the clock situation (as either the U2 or the R) and if this would have made any difference in your call on the final shot. We have agreed that the shot may well have been good in the 3.6 seconds, but it would not have counted in anything less. Of course, White would likely have played it differently too with less time on the clock. So do guys feel that all was done fairly? Thanks.

PS rainmaker, notice that this happened with 3.6, not 2.8!