The Shulchan Aruch holds that one may borrow and make a brachah on someone else's Tallis without their permission provided that you put it back the way you found it (OC 14:4).
In the previous halachah, though (14:3), he held that if you borrow a Tallis that is missing tzitzis you only have to string it after thirty days, and even then only because of mar'is ayin, as the passuk says "your garment" and not that of someone else. Therefore only talleisim that belong to you are obligated in tzitzis. Why don't we make the same derashah in 14:4 to exclude a borrowed Tallis from the mitzvah of tzitzis?