I think the writer is under the impression that Twitter is using a 32-bit signed counter and will start using negative ids when it rolls over. Evidently some people on the linked Twitter development thread had the same misconception. Actually it looks like Twitter is doing it right: they're just going to keep counting up past the maximum 32-bit signed int (after skipping a bunch of ids to move the Twitpocalypse up into business hours.)
It sounded like the problem wasn't Twitter, but 3rd party Twitter clients. They have no way of knowing if these use a 32-bit or 64-bit ID field, so if Twitter sends back an ID that can't fit in 32 bits - what happens? Do they crash? Wrap? Take only the low-order 32 bits?