Which is correct? I believe my answer is, yes. Of course it makes much more sense for it to be called football, as it is a game that you play with your foot and a ball, but I do live in North America. When in North America when I say football, unless it is with a wonderful British accent, you are going to assume I am talking about a team of 40 running around in tights hitting each other with a lot of breaks, replays and advertisements. In this case I believe saying soccer is correct because it avoids confusion.
I think this is brings up an interesting concept, that when it comes to communication it is more important to be understood than accurate. The best communicators are rarely the ones with the most knowledge but rather those who understand how the human mind works. Those that understand how to articulate a concept in a way that the audience can grasp.
There is not much to it other than I found it interesting as I was enjoying a pint with a couple lads at the pub after my match on Monday. They had accents and when they said football, they meant soccer.