That's a perfect example; in my experience that kind of RNG state is global (or at least, it has all the problems of traditional global state). Potentially any object might behave in a strange way, because it contains a reference to that RNG (hidden from you): you might find a sequence of calls that usually, but not always, reproduces a bug in test, and then it turns out that it depends on whether other tests running in parallel are affecting the RNG state. Essentially any test you write that's bigger than a single-class mock test has to be aware of the RNG and stub it out, even if you're testing something that on the face of it has nothing to do with RNG.

In a functional program you would make the RNG state an explicit value, and pass it where it's used (but not where it isn't - so there might be large program regions that don't have access to it). It'll be an explicit part of the top-level state of your program. I'd argue that that's not actually any more global - or at least, it causes fewer problems - than the OO approach.