The point here is not concerned with the specifics (which is what Tilt seems to be caught up in) but that for anything to 'exist' it must remain so for some period of time, or else it cannot be said to be, for it is already something other. Flux presumes perpetual change and that breaks the principle of self identity, for if flux were true, then nothing would in fact exist, because it would not 'be' at all, it would be otherwise.
Now you might say that flux is true in the scientific sense that things are in perpetual motion at a minute level that is far beyond our perception. For example that a chair may 'appear' to be the same chair it was a minute ago, but it is changing all the time, at an atomic level (or however you want to slice it). However to us, the chair remains the same until it changes. So we have a problem, we can either assert the existence of the chair, or we can deny it. To assert the existence of the chair, to say that the chair exists in my experience is to deny the idea of perpetual change. To deny the existence of the chair is to say that although it 'appears' to be a chair, it is in fact in perpetual flux, along with the rest of our world, and we do not see that because we are ignorant of the Buddha's teaching. Now if you re-read the first quote, you will see that this is nothing more than the two contentions that the Mahayanists make. It is the same argument, unfortunately that Orthodox Theravadins make.
In light of the above, this should now make sense. If it doesn't, I'll try to expand when I get home later on.
This does all make sense to me (if I understand it correctly, and I think I do) but the bit I have bolded seems to me to be a typically (perhaps specifically) European dichotomy: A or not-A, with no other possibilities.
There are, in fact, other possible positions to take: A and not-A; neither assert nor deny A; the 'unanswerable question' position. The second and third of these arise repeatedly in the suttas, though I'm not sure about the first. There is also what I think of as the pragmatic contextual response (it probably has a better name) which is that if thinking of A as existing is useful at the moment, consider that A exists; if not, not. It's actually my preferred position, FWIW.