The implication I always got was that non-living material was destroyed, not that it was left behind. Unfortunately, I don't think that we've ever really gotten to see what was left behind after a time-jump before.

But yeah, by that logic, shouldn't Cameron and the Turk machine have been destroyed when John and Weaver jumped forward? Unless Cameron's organic components still counted, in which case she would have gone with them. For that matter, I can't recall what we can see of the basement room after they jumped, but it seemed rather wreaked.

(If they'd just put the time machine far enough away from John Henry's table to not engulf all this other stuff, then they could have avoided this problem.)

I'm all for the "John Henry didn't go to the future" theory, if only because him going to the future is the worst move he could make: as I've said before, it makes no sense for John Henry to face Kaliba/Skynet in the future where its processing power will have increased by several orders of magnitude and it controls armies of Terminators and HKs that can act openly, instead of in the present where they're more even matched in processor speed and it has only a small force of Terminators and human mercenaries that must act covertly.