>underlying physical phenomena (described via quantum mechanics) is fundamentally random
This is one interpretation of QM. There are many theories explaining eigenbasis collapse (the "random-looking" phenomenon), and some of them are deterministic.
The important thing here is that the data stream is hard or impossible to predict. It doesn't have to be truly random, because we don't even know if "truly random" is a sensible thing to ask for. What we're actually hoping is that you can't predict the result of a measurement, whether or not it's because of randomness or something else.
Most RNGs also don't rely on the uncertainty principle (or, more generally, non-commutative measurements), but instead on e.g. radioactive decay. This is an eigenbasis collapse mechanism (with the two eigenstates being "this thing hasn't decayed" or "this thing has decayed"), but it's not based on uncertainty. This is easier to build physically.