Voyager is never coming down. Even if we wanted to bring it back, we couldn't in this century, maybe ever.

Eventually it's slagged remains will find a black hole to rest in, which is a different down at best, but even the black holes will evaporate, assuming the universe lasts that long. This fate is so far beyond the concept of down that there must be nuance in the claim, especially when talking about astrophysics.

Every interplanetary craft defies the phrase, and even orbit demands a deeper understanding. "What goes up must come down" sounds good and covers everyday life, but just like Newtonian physics it breaks down at large scales.

Something axiomatically correct would always be true (for the axioms we have taken). Perhaps you could take "On Earth" as an axiom here, but that's a very restrictive axiom that you need to specify. Thus a more nuanced take: "What goes up must come down, unless it leaves the atmosphere."

Not that I'm using axioms very rigorously. They're usually used for math things. My informal usage was to evoke the sense of absolute truth. Of a statement so obvious that it doesn't need proof. I find Tyson speaks in terms of "this is" rather than "this suggests" or "we have evidence for". He speaks like an omniscient narrator speaking a story rather than a communicator of science.

Also, 'Falsity' is a word, and I think you're actually using it correctly; it's the opposite of 'Veracity' and also a noun for a lie or untruth. "The falsity of the statement" seems right, but it's also old and very underused. I think a better word would be 'Falseness', but 'Falsity' in neat!