This happened to my DH when we were living overseas. Another kiwi struck up a conversation, found out they were from teh same city, then wanted to know what school he went to. DH was in his 30s for pete's sake! Maybe it was the highlight of this guy's life, I dunno.
Anyway, I don't think it's important. It does seem that some graduates of private schools seem to think it's important - maybe it's drilled into them at the school - but I really can't see how it could possibly matter.