you are supposed to use a back up method for the first month, although if you read (and trust) the fine print supposedly you should be good after about a week (I wouldn't trust that, personally...)
My pill said one week too, and I think you can trust that. Since you start taking the pill while you are in the middle of or just finishing your period, you start building up the hormones before your body could possibly ovulate again. I assume the one-week just gives your body time to get the hormone levels stabilized and for the other element of the pill, the thickening agent, to build up.