No, that is not true. In fact, sex a few days after a female's period ends is actually within the most risky time. While it's not true that a woman can get pregnant anytime she has sex, it is true that unless she charts her fertility, including basal body temperatures and cervical mucus evaluation, she cannot be sure what her safe and unsafe days ARE, so anybody who does not have this information must assume ANY time sex happens, it can result in pregnancy. Sperm can live around 5 days inside a woman. So, let's say her period last for 5-6 days, and you have sex 2 days after it's over. Those sperm can stick around for around 5 days, so they could stay active up until day 14-15, which is the average ovulation. Women ovulate earlier or later from cycle to cycle, too, which makes timing intercourse around a set ovulation period useless.
So, you'll want to choose a good method of contraception to use at all times. FAM and withdrawal are not recommended by us for teens. An excellent, easy, inexpensive choice with the least side effect is condom use. Used correctly, they're around 98% effective against pregnancy, whereas typical use of the rhythm (or as I like to call it, guess-timation) method is 80% or less.
I'm going to link you to a few good reads around the site, the most important of which is the choosing contraceptives article: