Another option is to "shoot the moon":
Tell your girlfriend EVERYTHING YOU OWN IS FROM AN EX GIRLFRIEND. If she gives you any trouble, just lift an eyebrow, and ask plaintively "come to think of it, what have you done for me lately?"
I totally agree that giving up the boxers, in the pragmatic scheme of things, is a great way to defuse an isolated issue. But it's also the slightest sliver of a sign that your girlfriend may have over-arching insecurities that will, in the longer run, cause much larger problems in your relationship…
Assaid, it's old underwear versus sex. I'd simply argue that at some point in many relationships, the old boxers win that fight – and if you ever foresee that being the case down the road, then you're best off ditching your girlfriend now before you run completely out of comfortably tasteful skivvies.