The game you were trying to remember was Xavier - Kansas State. KSU was up 3 and tried to foul but the ref didn't call the initial foul and then did call the foul when the Xavier player was shooting the 3. That gave Xavier 3 FTs to tie the game and they did.
I don't understand why the defense just doesn't jump in front of the offensive player when they are dribbling up the floor. If they get called for the block, that's OK, because they wanted the foul. If they get the charge, even better.
That said, I think the team ahead by 3 should foul in every case at the end of the game. It is the best percentage play, IMO. As SR said, the team has to do 4 or 5 things correctly just to tie the game.