Well if you look at this video review at 2 minutes 41 seconds, this Galaxy Nexus displays and scrolls a pretty heavy website in desktop mode flawlessly, and this is when the Gnex first came out in reviewer's hands, with the stock firmware of course.Whoops, sorry. In any case, I'm running 4.0.4 (yakju) and it's definitely happening. Since I definitely have the Nexus and it's completely clean (I've disabled about 60% of the default applications) I don't believe your friend. Well, at least if he is running a stock ROM and the stock Android browser.
I'm usually the first to criticize a product like the iPhone or a crappy Android phone but to say that you can't view a simple thing like a desktop page on a phone with a dual core processor is just silly.
http://www.youtube.com/watch?feature=player_detailpage&v=VeZ8sfJjoRI#t=241s