the truth-value of the claim, which is what we're discussing here

More precisely, it's what you're discussing. (Perhaps you mean I should be!) In the OP I discussed the implications of an infinitely divisible system for heuristic purposes without claiming such a system exists in our universe. Professionally, I use Newtonian mechanics to get the answers I need without believing Einstein was wrong. In other words, I believe true insights can be gained from imperfect accounts of the world (which is just as well, since we may well never have a perfect account). But that doesn't mean I deny the value of worrying away at the known imperfections.