As with any issue, we need to clearly define what the claim is. Fatigue, like many other factors, is not black and white. The claim from the UCF thread seemed to be that resting players 5 minutes so they aren't playing all 40 will improve performance in the future. That's a specific claim, but it's not testable. We have to rely on intuition.
As to your examples, fatigue could play a role in all of them, or it could play no role. That sounds cliche, but it's true. Cronin already admitted today that Gary was not tired against UConn. He was apparently trying to protect his injured mouth. But even Cronin doesn't know for a fact whether Gary's performance suffered from fatigue, and Gary himself probably doesn't either. No data is going to help either.
Against Florida, we lost for a variety of reasons. To my eye, the most important was it took us way too long to adjust to Chiozza isolating our small guards and backing them down. Possibly the week off played a role, but there's no real way to tell. If we played that same game 9 more times, we might win 6 of them. Trying to draw conclusions about anything from any individual game is difficult.
Evans' shooting percentages over a 3 game stretch are purely anecdotal in my opinion. There's way too much variance to say anything with that small of a sample.
The Jackson case would probably be better served using a metric other than shooting, since his effectiveness was not necessarily measured that way. Regardless, that example also suffers from small sample size, and it's not controlled for anything at all.
There are different philosophies regarding rest among coaches across college and NBA basketball. And each philosophy is valid because there is no conclusive evidence regarding the effectiveness of rest.
Personally, I think rest is pretty insignificant from game to game. If a player has a sore joint that needs to heal, then keeping him off it as long as possible will help. But I really doubt that giving a healthy Evans 35 instead of 40 minutes is going to do anything for him. And I also doubt that playing Florida after a week off had much to do at all with why we lost. But I can't test those ideas, so they remain opinions.