It would matter in that it would choose other 'american' civs for your randomly-selected enemies. It's possible to accidentally click that option on; I've done it myself. Try starting a new game and look at the options clicked off on the second page of the 'start game' dialog (the screen titled PLAYER SETUP) - if you've accidentally clicked that option ON in the past, it will be ON until you start a game where you've clicked it OFF.
I almost always start with America as the human player; my current game is a 'standard' sized map with 11 randomly-chosen rivals, and I don't have any other American civs as rivals - and that's unusual, since there are at least 4 other American civs.
If you want to post one of your saved games, I'll look at it with one of the utility programs that shows what options are 'on' (I use the Civ3 Multitool Save Game editor).