Paul Powell left out one detail, though perhaps it's easy enough to figure out. If you use the same key twice, it is once again possible to determine key by trial and error, since chances are only the real key will make BOTH messages intelligible.
And whether quantum effects are "truly random", is a question best left to philosophers I think. It doesn't matter for this. Even with some currently unknown theory of quantum mechanics that does away with the randomness, trying to reconstruct a the state of their hot tea, quark-by-quark, in order narrow down possible keys would be... unfeasible, to put it mildly.