I guess we'll find out more tomorrow when DSP does his usual 2 hour pre-stream, but I think the odds are in his favor. More often than not, PayPal sides with whoever makes the dispute as long as they can supply the barest minimum of proof. Even if you aren't purchasing and were just sending money to a friend, which is most likely what Tut classified it as to avoid PayPal's transaction fee, you can generally dispute it and just say you accidentally put in the wrong amount or the payment somehow processed twice.
One of the few situations where PayPal is unlikely to side with you is when you have a history of making payments to someone and now out of the blue you're claiming the most recent payments are invalid. If there were some sort of product attached to it, Tut could use that as evidence to support his claim, but without that, Tut doesn't have much of a case. If anything, it might even raise some red flags to whoever is investigating it and thinks there's some sort of scam going on.
It largely depends on how much/how frequently Tut sent Phil money. It also depends on how much Tut pushes it. If he gets through the automated hoops and actually speaks with a real person then it's up in the air depending on how much work the person feels like doing, as well as what Phil does to dispute the claim. But, I wouldn't be surprised if it boils down to a repeated cycle of asking Tut to provide evidence of failed delivery, and given that Tut isn't the most articulate person in the world, I don't know if he'd do a decent job explaining himself. Even if he does, if he brings up anything Twitch related, they'll probably just tell him to take it up with Twitch just to get him off the line.
Regarding any sort of stream evidence, no customer service rep is going to care about that, especially not someone who isn't affiliated with Twitch. In terms of our general amusement, I think the best case scenario is PayPal temporarily suspends both of their accounts while they look into the claim. This is outside my general PayPal experience, but I've heard over the last few months they've gotten more vigilant with going after suspicious accounts, with tipping setting off a lot of automated red flags. Before, if you jumped through a few hoops and actually spoke with a person, they were pretty quick about restoring your account, but they might have gotten stricter about it in recent months.