I see zero evidence outside of a tiny CBlog poll that the Celtics will hesitate to pay IT the max. He's easily going to make that, he nearly won the scoring title, he made 2nd team All-NBA and he's in his prime. Crazier things have happened, maybe he gets traded for Paul George or some other star, but it's a pretty safe bet we're not letting him walk.
As for Bradley, we're under a larger cap with more spenders than the one that signed Evan Turner to a $70M deal. We shall see what offer he actually gets, but my argument would be the same if he gets $20M instead of $25M. He's going to cash in and much lesser players will make $15M+.