so we are all in agreement that coach coming onto floor means we have no discretion to keep injured player on the floor, we must sub them out even if it is late in the game and they are obviously only briefly injured, maybe contact had to be rearranged, maybe they lost their wind, whatever, and now the coach has his best player sitting ready to come in and shoot the free throws? We cannot stop coach from coming on the floor, at least I cannot find anywhere where it is a Tech for a coach to come onto floor to help semi-injured player; so that means coaches can use some gamesmanship late in games to get best shooters to the line and nothing we can or should do about it?

just have not heard any opposite opinions and I had this happen last night and felt helplessly at the coaches mercy whether he decided to come out or stay on bench

NO, SIR!!!!!!!!
The coach is NOT allowed onto the floor unless beckoned by an official.

See 10-4-2 ". . . Enter the court unless by permission of an official to attend an injured player."

Also, displacement of a contact lens is not an injury. The player is not subject to rule 3-3-5. You can grant a time-out to the player in this case and it doesn't even get charged to the team. See 5-11-3 Exception a.

Also, whether or not the coach actually comes onto the floor doesn't matter. It is whether or not the official BECKONS the coach or other personnel onto the floor to attend to a player that matters.

So, if you beckon him and he refuses to come aid his player that player should still be directed to leave.

but Rule 3.3.5

A player who has been injured to the extent that the coach or any other bench personnel is beckoned and/OR comes onto the court shall be directed to leave the game, unless a time out is requested by and granted to his/her team and the situation can be corrected by the end of the timeout.

which indicates to me that a coach can come on the floor when unbeckoned, am I reading that wrong?

Well, your reading is fine, but you are understanding it incorrectly. The coach or other bench personnel MUST be beckoned or it is a technical foul. 10-4-2 is quite clear about that.

The OR part simply means that the player must still be directed to leave the game even if the coach comes out without being beckoned and is thus charged with a T.

You see? The coach can't run out there without being beckoned, take the T, and try keep his player in the game. That is why the word OR is in the rule.

While this is the rule, I've never seen a T issued for it (if there's any chance that the player is injured) and I've never seen a coach try to get a better shooter in by claiming that a player is injured.

If the defense is really "going for the ball" and makes a reasonable (as ooposed to "hard") foul, the chances of a player being injured are small.

If you suspect a coach of doing this, write the state.

For the record, I'm not advocating whacking a coach when he comes out to tend to his injured kid, if that is what he focuses on doing while he is out there.

I was merely informing the questioner about the actual rule since he asked.

Are you refering to NFHS or NCAA 10-4-2? Had this discussion with my Officials Clinic coordinator (trainer) and he told me that the Head coach need not be beckoned to tend to an injured player. I must have looked very puzzled at him because he told me to go look it up in the rules, and referenced 3-14 in NCAA rulebook. Personally I would have neve had to T up a coach but have booted the substitution once.

Thanks