Mint typically spreads by the roots, similar to oregano and thyme. I doubt cross pollination is the problem.
Although it sounds somewhat unlikely per your description, it is possible that you may have a look-alike weed in there. I've got some weeds around that look very similar to spearmint or peppermint but don't smell or taste. The particular weed I'm talking about (I think it may be a type of "selfheal") is more agresive than spearmint, beleive it or not....
Rick