I don't think you're being charitable here. Sure, their explanation wasn't perfect, but their line of reasoning was absolutely on point.

You almost gave a really good explanation yourself on why this should be the case but stopped short of it. Don't know why. Any terminating decimal can be written in the form a/10^{n} where a and n are both integers. After we have our p/q, there exists an integer c such that p/q · c/c = p/10^{n} if and only if q consists solely of the primes 2 or 5 (or both). And if not, then there isn't an integer c to satisfy said condition, thus making it impossible to write our p/q in the form of a/10^{n} (white still keeping the numerator an integer at least) so it's an infinitely repeating decimal.

You're right, my explanation was invalid.