Why Don't Teams Up By 3 Foul?

I need to figure something out. And I've needed to figure it out for a while. But this blog finally gave me the forum to ask the question. Why don't teams, when they're up by 3 points and only time left for one shot foul? Why do they give the other team a chance to hit a 3 and tie it up rather than foul and make it almost impossible for the other team to tie it up?

This happened in the Siena win over Ohio State. Ohio State was up by 3 points with time for one shot for Siena at the end of the first overtime. Instead of fouling on the Siena players, Ohio State allowed Ronald Moore to tie the game with a three (they would later also allow him to beat them with a three in the following OT which is a problem in and of itself).

So how could have this been avoided? Ohio State should have fouled Siena before they coucould attempt a shot. This way, the maximum amount of points they could have scored was two points. The chance they would have gotten another shot at the ball is minimum. They would have to make the first, miss the second, grab the rebound and score. The degree of difficulty of this is MUCH higher than making a three pointer.

Although it makes all the sense in the world, this doesn't seem to happen many times if ever. I'm not sure if Thad Matta sent his Buckeyes out there to foul, be he should have. Coaches are always worried about criticism that their methods will make the game boring or criticism that they're stopping the clock. But the point is not to avoid criticism, but to win, so I think more teams should think about fouling at the end of the game to preserve their leads.