I think being a brilliant musician (concert level, say) would garner nothing but respect, but telling everyone that you have Grade 8 piano would likely be seen as bragging and, depending on the situation, rightly so.
There is a balance to be struck between being gracefully modest about your abilities (a truly intelligent person is acutely aware of his or her limitations, and how much he/she has still to learn), and having to be over-modest for the sake of keeping the peace, or because you don't want to seem like bragging just for uttering a simple word like 'Oxford'. When asked what I do, I tend to say I'm a postgrad. When the inevitable 'where?' crops up, I feel myself cringeing at having to say Oxford, unless I'm speaking to someone big enough not to have a problem with it.
Usually, when I answer the 'where' question, suddenly the conversation turns really sarcastic, with the other person saying 'Oh, so you're a brainy one are you? Well, I didn't realise I was in the presence of greatness' - or worse, they think I'm upper class and loaded. I could always lie, but that would be the lowest thing to do - as you say, why hide it, as if ashamed, just because some idiot is going to judge you?