This is incorrect.

True random (vs pseudo-random) relates to whether the past outcomes of the generator provide any information about the future invocations. There is nothing stating that a true random generator can not conform to some distribution

There are cases where you might not want a true random generator, although this relates more to the importance of unpredictability versus the performance requirements for your domain.

Or maybe a more succinct way of putting it. You can sample random numbers from any distribution. There's nothing special about the uniform distribution except that it's one that people want most of the time.