Can he do anything to change this mentality of students and staff?
Moving out won't help now that the voice has spread. Looking stingy in ordinary expenses will further stereotype you into a Scrooge Mc Duck type, so do not try to overcompensate by saving pennies. Just live a normal life. Do not drive to campus in a Lamborghini or a taxi, but do not reuse tea bags.
I am afraid it will take time and personal interaction to fix this and get across one's real personalities. Stereotypes exist exactly because they are easy to form.
On the bright side, as far as stereotypes go, it's not a particularly bad one.
Is extended-stay hotel this un-ordinary for academics and students?
For students, in my experience it is quite unusual. In many universities there are student dorms, of course, but they are aimed especially as students and they are a different thing.
For academics, it is more common; see below.
Don't visit academicians that visit just 6 months' stay there?
Yes. 1-6 month visits are very tricky to arrange from the logistics point of view: too long for a hotel, too short to make renting an apartment convenient. This kind of furnished accommodation is a godsend.
Nowadays these visits are reasonably common, but it is not unheard of that some academics, especially older ones, never went to one or hosted a long-term visitor. You basically need a semester free from teaching to do it, and once you have a family a long trip is a lot more tricky to arrange.
For this reason I would suggest you not to worry about faculty; things will fix themselves, and most faculty at least tries to be objective and not let these stereotypes influence them. For your own social life, convincing students that you are not Paris Hilton is your #1 priority. How to do it is is off-topic here though. As another stereotype says, we academics are not so competent about social interaction. :) So treat also my first paragraphs with a pinch of salt.
I would suggest you to head over at [interpersonal.se].