Actually, we do need evidence for premises which are not definitions or basic assumptions (axioms). Graviton is still a hypothetical particle and falls under neither of two categories - Definitions or axioms.
The only way this statement could be false would be to have quantum gravity but no particle that mediates this interaction - which doesn't seem plausible almost by definition.
That's quite an exotic claim! If Sound and Temperature can emerge without a sound particle or temperature particle, why is it not plausible for gravity to exists without graviton?
Though, I get it that mainstream view from physicists is Graviton is the most 'likely' cause, if the gravity is proven to be quantized. But even they would have the humility to accept that this is a theory yet to be proven and observed!
A: If gravity is quantum, then (B) there must be some particle-like think that we call a graviton that mediates the interactions, and then seeing a rubidium atom fall must have been an interaction with this particle.
not A: If gravity is not quantum, then they are making no claims about a graviton.
If you think gravity is not quantum, then you go to the "not A" branch, and they make no claims about that branch - so there is no contradiction with their IF.
However, for me to claim that quantum Gravity is only emergent without a particle like graviton's mediation, I would need to present evidence. Just like this claim - quantum gravity is only possible from gravitons.
Now, as to how plausible this is, we'll actually get into semantics. To me, saying that "gravity is quantum" would mean that it is a real force/interaction, and that this force obeys the Heisenberg uncertainty principle. So, I wouldn't say "gravity is quantum" if it turns out that the Entropic gravity theory is true, as in that theory gravity is only an apparent interaction. However, I admit that this may only be my perception of what these terms mean together, and that others may use "gravity is quantum" to refer to any theory that explains the macroscopic effects we call gravity in a way that matches quantum theories.
If I am understanding your counterpoint correctly, then this argument can only be concluded satisfactorily if either Graviton is observed (proving is existence) or something more fundamental and deeper is observed (proving that quantum gravity can emerge without graviton).