In my experience people with a genuinely high IQ go out of their way to avoid mentioning it since it only creates problems. The last thing to do in any circumstances is to make others feel inferior, or to imply that they are, and that is one of the first things learnt - often through pain or bullying - so high IQ people often tend to be somewhat withdrawn socially and may be poor at expressing themselves in a social setting.
Not only that, but studies have demonstrated that individuals (especially children) listed as 'gifted' are often less satisfied in life, and end up dropping out rather than contributing in some big way. That feeds into the 'minimizing my intelligence' rather than bragging about it. If it brings you no happiness, and makes people think you're an egomaniac, why the hell mention it to anyone.
DocHoldiday has some good points, but I don't really see their relevance to the basic question. Yes, there are all sorts of intelligence, but we're talking about someone claiming an extremely high IQ when they can't support it with their writing. That doesn't suggest that others aren't intelligent, only that the claim rings especially hollow.
Just as you've got to be careful writing from the perspective of a Nigerian transvestite during the Ebola crisis, you need to be extremely cautious about any perspective you have little basis with. If you don't know anyone with an IQ that high, what makes you think you're qualified to represent them? Research helps, but more important than research is understanding their perspective. Being able to claim your character is smarter than everyone else is a self-serving fallacy.