"Does everybody agree with that assertion or do you think I'm full of it" - He's full of it. The signal is not "bouncing" off the satellite, you don't need the satellite to be perfectly between you and the person you are communicating with across it. Rather, it's separate and simultaneous send and receive actions. You need to be able to reach the satellite, and the next communication point (whether another person with a sat phone, or an interlink to a different communication system, or whatever) need to be able to reach the satellite, but the "angle" between you doesn't matter at all, which is why you don't immediately lose signal upon moving.
As far as the Van Allen radiation belt... the guy is a total nutjob with a degree in pseudoscience. The reason the satellite is on the inner side of the Van Allen belts is because it's a) a lot easier to fix or replace that way, b) they're very thick, having a satellite say 640 miles up vs having it 3000 miles up means lower latency and better communication, and c) you don't want to hang out indefinitely IN the Van Allen belts. But they don't block communication to any meaningful degree. And about the idea that they're "thousands of degrees" - it's space, dude. The Van Allen belts are not a greater concern as far as heat transmission to the interior of a rocket or whatever than say the raw un-atmospherically filtered power of the sun, or the heat generated on reentry. They deal with heat all the time, the Van Allen belts are not a major concern.
And as far as how the signal "magically" gets there... it's the same "magic" that lets the sun's energy reach us millions of miles away, or the same "magic" that lets us see galaxies other than our own. Barring dispersion, signals travel indefinitely. The thickest part of the atmosphere is the biggest issue, you communicate first to a satellite, then from there it's transmitting out (yes, through the Van Allen belts, they're not some impenetrable shield), and as long as there's either straight point reception by the target, or something it can communicate with which has straight point communication, you're good. In the case of Perseverance, it communicates with Odyssey, which is in orbit around Mars and serves as effectively the "satellite" he's talking about.
I loathe that kind of person - he asks a bunch of rhetorical questions, that have answers. Ones which are readily available as well. But instead of learning or seeking how things are, the moment he encounters something outside the scope of his understanding, he goes to "nope, impossible - if I can't figure it out, no one can".
Edit: And as far as his "how would it be possible for it to survive reentry" bit, RCC (Reinforced Carbon Carbon) panels. That's why Colombia blew up, one of them failed, and indeed they're kinda important. But yeah, not an unsolvable problem, and again, readily available information for those who take the time to look into it.