(1) There's no indication that there was any overheating due to the prior incident. In fact, the probability is that, since it was a roadkill accident which destroyed the radiator, the engine was immediately shut off. Very unlikely that there was any overheating at all under those circumstances.
(2) Overheating only very rarely affects the block. The chief symptom of overheating is a warped head.
(3) Oil starvation will affect the valvetrain far more than it will affect the block, even the cylinder liners. This makes it at least plausible that the majority of the damage is in the head making it cheaper and faster to just replace the entire head/valvetrain with a rebuilt unit. The cylinders can simply be honed and the pistons re-ringed in most cases which wouldn't require replacing the block. Even if it spun a rod bearing, you still wouldn't need to replace the short block.
(4) None of this changes the fact that what he's going to get back is, for all intents and purposes, a rebuilt engine. The only difference between the shop repairing it using a rebuild from a different supplier is that in his case the core is his own engine, not some random core from another car.
Now, that said, if you want to say, "I don't trust the mechanic to do a good job," that's an entirely different issue. That's fine. But if the mechanic is competent, then there's no reason to prefer someone else's rebuild over that mechanic's.
ZV