"if someone, on the outside, feels that such a thing exists, then it probably does"

I could not disagree more. The perceptions of a person frequently have absolutely no connection with the reality of a situation. Nothing, repeat, NOTHING we can do, say or attempt will prevent some people from feeling that a "clique" exists.

A person may feel that there is a clique which is excluding them; but the reality could well be internal feelings of inadiquecy, inability to communicate, inability to share, lack of interest in subjects, etc. etc. etc.

Unless there is INTENT to exclude, a clique cannot exist.