The answer is simple.
There is no rule preventing an older player from participating in Summer League. It has nothing to do with Sully's weight, back, or conditioning. He was practicing with the Summer League squad all last week. It doesn't have anything to do with not needing to prove himself either.
Silly wanted to play. He asked to get reps with his younger teammates. That's why he was allowed to practice with them. As far as games, the Celtics simply said no. They wanted to give the minutes to guys like Smart and Moser and Iverson to see what they've got, and guys with non guaranteed contracts for next season like Pressey, Babb, and Johnson. They could let Jared dominate SL, or they could see what everyone else has got. That's all. They just said no.
Speculate if you will about anything that's been brought up in the previous 4 pages, but that's really all there is to it.