很多北京人喜欢说认识名人 ------- Knowing some celebrities does not necessarily mean they have a real relationship with them, say for example, I know you Sabre, as a forum celebrity, but I am not engaged in any relationship with you, in reality or virtually; and please do not get offended by this, just an example. I have a long but very good shot at you.
In this sense, when some say "they know somebody with fame", I will just take it as a fact without questioning. I suppose the "feeling of comfortableness" has an underlying implication: knowing someone is equal to having the ability to achieve something through a relationship with that someone, which is not valid, in my humble opinion.