My friend studies at a very prominent university and has invited me to visit her. Coming across the university shop, I was thinking whether to buy one of the t-shirts with the logo.

I possibly am over-thinking it but the following scenario popped up in my head: What if, while wearing it, I'd be approached by a person who'd think I went to the university, and who'd ask me what my major was, etc. And when I'd say that I wasn't affiliated with the school, wouldn't it look like I'm taking a credit for what I haven't done?

Does a university t-shirts implies that the person wearing it was/is somehow affiliated with the university?