Does wearing a university t-shirt imply that the wearer is 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.