The photos suggest otherwise.
He appears to be a walking definition of over-sized ego.
Actually the person you're replying to is right - in so far as we know from people who ACTUALLY know Nick Grimshaw, as opposed to tabloid hack jobs and People On The Internet. Matt Fincham (his producer) has commented twice on his lack of ego, the first time they'd just moved studio and Nick jokingly asked if he'd wrangled it by saying Nick was demanding they changed. To paraphrase Matt, that wouldn't work because "everyone knows you're not like that, you're a nice guy". Add that to all the Call or Deletes when Nick tries to get celebrities to say getting the Breakfast Show's 'changed him' and turned him into a diva and so far not a single person has believed them. In fact they usually protest quite strongly that he wouldn't act that way (I particularly liked Caroline Flack's "Grimmy woudn't do that, he's everyone's friend" to Olly Murs). I have yet to hear anything bad about the man from the people who know him and spend time with him (of which there are a lot - perhaps because he's fun and a good friend? Just a crazy thought!)