What bothers me about that story is that the person telling it had insisted, loudly, that there was no offer made, whatsoever, period!
So I guess you can chose to believe his admission that he was lying before.
I also do not find his new story different in any meaningful way to Kraft's story. Kraft came on strong to refute the contention that the Patriots had made no offer to Wes. Then he said that they had made a good offer (apparently the take or leave it offer) and that Wes had turned it down.
Once that happens you move to plan B, since if you wait and wait on plan A forever then you miss out on plans B, C, and D.
Then 24 or 48 hours later when plan A comes calling again, after plan B is all wrapped up, you shake hands, say "sorry dude, too late" and move on.
Business is business, and that's how business is done.
Timelines, decision points, and go/no-go decisions.
Big boy stuff.