3 uses.

1. Impervious to fame. As in doesn't let popularity go to one's head. A

celebrity who doesn't act like a celebrity. Not pompous, stuck up or

conceited.

2. Unable to achieve fame. Such as someone who is so devoid of

talent, class, standing or ability that they will never achieve fame.

3. Someone who is so beyond the norm as to be beyond the aptitude

of fame. Someone who is too controversial, too far out, too beyond

the average to get accepted in the main stream. This would be the

opposite of the 2nd usage in that the assumption here would be that

this person has too MUCH talent to be famous, as opposed to too

little.