This is a straw man, and I think you know that. It's more like saying Atlantis doesn't exist, and, well, to the best of our knowledge - it doesn't. I'd be happy to re-evaluate upon receiving evidence that Atlantis may have existed, just as QM physicists should be happy to re-evaluate when sub-Planck-scale phenomena can possibly be observed using a theory which is also consistent with the rest of our observations of the world.
Oh and an even better analogy than Atlantis - it's like someone saying Australia didn't really exist when we couldn't observe it, and claiming they would prove it by sailing from Chile to Africa without encountering any large land masses.
So no, he's not making any weird philosophical claim at all.
I don't see much difference. If you're "happy to re-evaluate" (e.g. open to the possibility) then the answer (even re: Atlantis") is "I don't know if it exists", not "doesn't exist".
Actually what you say is the weird philosophical claim.
It's like saying Australia didn't really exist when we couldn't observe it (or see any effects from it reach us).
The thing is, to say it could be continuous even if that's not observable might be wrong. But not because it can't be both continuous and not observable: just because it can also be discreet and not observable, and we can't tell which of two it is for sure.
Whether we (or any observer imaginable) can observe effects or not, doesn't mean it's not one or the other.