2007 runs with no issues on XP 32bit, it's on 3 laptops in my home right now on that OS.
Try to return it anyway, they may not allow a full return, but I don't see why they would deny an exange. If you have an issue with the store, call MS and see if they can get you a valid 2007 key to use since you can't install the 2010 you bought.
It does not only work on 32 bit systems, but for some reason it does not work on XP 64. It works on Vista and Win 7. The issue with packaging is that I have yet to see any type of warning or system spec listed in big bold letters on the front. If I buy a new car, it does not say on the front page of the manual "Warning, this thing will start breaking soon as the warranty is over", they just say what a great car it is.