In my view, the only legitimate reason for Kraft to back down (not saying this is the case, but it's basically the only possibility where he isn't a complete coward) is if other large market owners (or a majority of owners) were threatening to blow up the CBA if the Patriots continued to dominate in what was supposed to be an era of parity.
Given the hostile response from those who ought to know the Wells report was junk (other owners & coaches), it's plausible this was about the other owners/teams demanding Goodell find a means of leveling the playing field, or else.
I wouldn't put money on that explanation, but if that threat were conveyed to Kraft via Goodell on behalf of the other 31, I wouldn't be entirely surprised.