To take a player attempting a 3-pointer from so far away from the basket that the odds of making the shot are 1 in a 100 (or less) and put them on the free throw line where their odds are 50-90 percent is not being fair to anyone. If you make a call like that you have just provided a very distinct and very large advantage to one team.
A foul is a foul and I don't think we will find anyone on this forum that disagrees. However the original scenario we were disucssing, I interpretted as two players fighting for a rebound and one coach screaming that he wanted three shots because his player was attempting to throw the ball the length of the court with 0.9 seconds left... or something like that. The immediacy of the situation is not my fault as an official. The immediacy is a problem for the team behind (they placed themselves there) and it is not my responsibility/position to help a team overcome that immediacy.
A foul call and a subsequent set of freethrows is an attempt to compensate for illegal actions, a foul. The compensation (freethrows) should be relatively commensurate with the loss. A possibly illegal act that removes a player's opportunity to make a 1 in a 100 shot should not be compensated with three opportunities to make freethrows.
This is the engineer in me coming out.... a 1 in a 100 shot => 1% opportunity to make 3 points. 3 free throws, assuming 75% success = 0.75 * 0.75 * 0.75 => 42% opportunity to make 3 points. I don't actually make calculations like this during a game BUT THESE TWO ARE NOT EQUAL by a very large, disparate amount. If you make that call, you are determining the game because you just provided a 40% great opportunity for that team to catch up. If you don't make the call you may have allowed the defense to illegally influence the 1% opportunity. For this particular situation I think it is better to allow the possible 1% influence than it is to assuredly CREATE the 40% opportunity.
The fat lady may not be singing but she is warming up long before the last second.