You can NEVER conceive a child while on your period. There are hormones in your body during menstruation that prevent ovulation, therefore preventing conception. HOWEVER, you can get pregnant as a result of sex during your period. Sperm can live in your body up to 5 days. If you have sex on the last few days of your period and are one of the unlucky women that have short cycles, it is possible. Highly unlikely, but possible. ETA It's also ridiculous to say "you can always get pregnant." That's far from true. Every woman has a 5-6 day window(depending on exact length of sperm life and length of time egg is viable) during which sex can result in pregnancy. Other than those days it is impossible for a woman to get pregnant.
Also no reason to be skeptical about ovulation tracking. It's much better to use it when you trying to get pregnant, rather than attempting to use it to keep from getting pregnant, it does work.