This is how the business world works. Sometimes you can't get the best deal, but it's still in your best interest to accept it regardless. You have to act rationally; you can't just defect (to borrow some game theory parlance -- this literally resembles Prisoner's Dilemma) in the name of "principles."
One moderately-crafted blog post later (saying Apple wasn't at fault, and he wasn't either -- his account was "only" linked to the other one), this guy would have been back in business. It's no surprise that this guy hasn't ever worked at a big company before, if you don't swallow your pride every so often and keep your mouth shut, you get kicked to the curb, and it's surreal that he was a self-professed businessman because of how often this happens in the game.
He WAS winning, and he would've won (nobody would've taken his PR damage control post seriously, and initially everyone believed his fabricated narrative of innocence), but he royally #$!@ed up because he thought he could've had his cake and eaten it too.
I can't under any circumstances imagine any possible outcome to this scenario where Apple would've both admitted wrongdoing AND reinstated his app. Let's not get too greedy here...
If anything, actually writing that something wrong happened would make it easier for them to justify their decision. It could be a trick representatives sometimes use when they assume the party they are dealing with is guilty. It's admitting to fraud and can hurt him more, especially if it didn't work out. And they can always reverse their decision.
If I had to guess, Phil & co. wouldn't want to risk that nuclear scenario (and they are definitely smart enough to know better).