I doubt the tyres or the fuel had much to do with anything. The driver in front still has the upper hand, being able to dictate pace and to drive in a defensive manner. With the aero this season, overtaking isn't easy unless the front driver welcomes the effort. In this case, Hamilton clearly wasn't anticipating Button to pull a move on him, hence the reason why he didn't defend until he noticed it (too late) that Button was doing an overtake.
As for pushing out - Hamilton had the inside line, just as Button did in the 2nd corner after his pass. Irregardless how close it was - from Hamiltons perspective, they were both saving fuel and not driving in a defensive manner and thus shouldn't have had to be in that position from the beginning. Given that they obviously get on well (Lewis and Jensen), I suspect he wasn't too pleased about being put in the situation where he had to retake his position in such a manner. His initial thoughts might have been also with the team who didn't inform him that Button was coming up, despite the "saving fuel" heads-up.