I think he had a helm in his pack and and he put it on when he knew he was going to fight. Afterall, how would you like to have a 10 pound block of metal on your head all the time? When he was aware of the orcs he got it out. My theory is he had it in a very handy spot in his pack.
BTW, when Tolkien wrote LotR, I don't think he had in mind people would start a big, long, debate on whether Boromir had a helm or not.