What OP is describing is the strong form of emergence, that emergent behavior cannot be fully understood or predicted by understanding each of the individual parts. Aka the whole is more than the sum of the parts. If you fully understood the laws of physics at an atomic level, would it be sufficient to recognize a cpu as turing complete if you see one?
It's a debatable position in philosophy against the reductionism OP is describing, and maybe a bit magical but I'd find it the more interesting of the two positions to hold.