Bodies experience many ups and downs. While it is unlikely that a woman will get pregnant within a day of starting her period, a number of unpredictable factors exist to ensure that you can never, ever say never when it comes to unprotected sex and the risk of pregnancy.
Generally speaking, ovulation occurs an approximate fortnight before the onset of menstruation. This offers a nice cushion between the two stages, but no woman's ovulation schedule is absolute. In fact, every woman - even the ones who can practically set their watches by their cycles - is subject to irregularity. As such, it is completely possible for them to ovulate early enough, or late enough, for their eggs to be fertilised around the time of their period.
Of course, sperm makes its own contribution to the unpredictability of pregnancy. While sperm normally has an average post-release lifespan of 2-3 days, it can survive in a woman's body for as many as five days. In other words, it can hang around up there just long enough to fertilise that early (or late) egg.
A general rule of thumb to follow in regard to unprotected, birth-controlled sex is that anything is possible... Except the complete elimination of the potential to get pregnant. The next time you hear that you can avoid both pregnancy without birth control if you time your sex carefully, don't pay it any mind. Dismiss the notion entirely. Birth control is your only "guarantee" against pregnancy, and even it is subject to error.