Robin Hansen explains:
“Illusory Power Transference” is the academic name for feeling powerful due to a superficial connection to a powerful person, such as having once been in the same room:
We propose that … associating with the powerful CEO suggests that he, too, must be powerful. Moreover, this minimal connection with the CEO would actually lead him to act as if he personally possessed more power when making important decisions on the job and interacting with others. ….
We use two experiments to … demonstrate that men who have a tenuous association with a powerful other (versus a powerless or equal-power other) felt more powerful and were more optimistic, confident, and risk seeking, even though they could not leverage the associate’s power. (more; HT Tyler Cowen)