Just by origin of the word polyglot means you have many tongues. Tongues is of course well established as a stand-in for languages. If you can speak more than one, you fall under the definition.

I think people have attached more to the term than just that though. I'm thinking of well traveled and culturally sensitive as well. Somebody who would be alright no matter where you dropped them.

How many languages can your better half say good morning in? She might just be trying to pay you a compliment and you with your humilis gloriatio are not having it. In any case, I wouldn't recommend going back to her with arguments obtained from a random group of internet users to settle your interpersonal disagreement.