Does wearing a university t-shirt imply that the wearer is affiliated with the university? My friend studies at a very prominent university and has invited me to visit her. Coming across the university shop, I was considering buying one of the t-shirts with the university logo. 

I am possibly over-thinking this, but the following scenario popped up in my head: What if, while wearing it, I am approached by a person who thinks 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 wearing a university t-shirt imply that the person wearing it was/is somehow affiliated with the university?
No. Many of the top universities are tourist attractions and it is not uncommon to see tourists wandering around campus taking photos and eventually buying paraphernalia. While in the US it is not uncommon to see students wearing standard school t-shirts and sweatshirts, in the UK, students generally do not wear clothes that are available in the bookstore. Rather, they wear clothes made for particular clubs that they are involved in.