1.Oh my god, it's not 5V either end, a floating power supply could have tens or over a hundred volts floating upon contact with another power supply if the two power supply are isolated for some time.
You do realize that when those two (isolated, floating) supplies are connected by only a single wire, then regardless of any hypothetical potential difference no current could flow and thus no damage to occur?
Or rather the only current would be due to leakage through the Y capacitor in the Apple supply, which would be very tiny (otherwise you would could get electrocuted). The C64 supply is linear, fully isolated with a transformer and no suppression caps, so unless the trafo is defective, no leakage current across it. So such current would have nowhere to go.
And once he reconnected the grounds, there was no more chance for hundreds of volts anywhere, because the two supplies stopped floating relative to each other.
The only thing that Apple charger could have potentially caused, depending on the C64 power supply design, is that the 7805 regulator in it could die because it has been back powered (he turned on the display power before powering up the computer).
However, that was unlikely the issue because he had problems even before he was playing with the displays and chargers (you didn't watch the entire video, did you?).
And yes, voltage regulators do die. I had that happen in a power supply for my ZX Spectrum clone - also a 7805. Those 8bit computers took quite a bit of current and it was common that these regulators ran hot (in my case regulating from 12V down to 5V, so some 6W power loss) and were dying from time to time.
Also Dave has a repair video or two where he is replacing blown regulators.
2.He used a newer model on the second try, it may have some bleed mechanism to deal with the floating voltage, or he connected the LCD before connecting the Apple charger, which could also solve the floating problem.
That "floating problem" is a complete red herring.