Not only that they could just say. "Why not just use the gyms healing machine."
Also, bit convenient that he the manual and all he needed to fix it in his pockets....
You generally keep the manuals near the machines, or stored somewhere. Some locations even keep the technical manual inside the device's chassy, if it's frequently maintained. It doesn't tell him if something small is missing. It basically tells him general information that is documented, and how to service it, or determine if it's in operational shape, correct operational voltages across certain components, and circuit diagrams where it can be serviced without needing to go back to the manufacturer... or be replaced. Which... without proper tools, you're not guaranteed to know until it's tested. So this machine could actually still be busted due to the prolonged exposure to heat. Just jarring it around won't do enough damage to it. Hince why he's a bit unncertain when he concludes that it may be fixed.
Best case scenario, The power cable was melted, and needed to be replaced. A few objects falling on it would have probably damaged the screen and glass. Worse case scenario, the heat actually destroyed something very small in the circuit board that it's hard to notice. It can still be salvaged, it just won't be availible immediately. Or a pillar had basically crushed it all together.
And to be honest, this is actually just a convenient excuse for my character to introduce himself to the others and not be a lone wanderer. If it wasn't for him knowing that your pokemon were hurt, and that the only center in town had been burned down, he'd probably would have moved on to the next town by personality - he's not very social and is more concerned about Maple's well being.
But... do gyms actually have a healing machine? You're generally forced to run back to the pokemon center, aren't you? I know the Elite 4 has them at the end of the journey.