Never heard of that.If that was true you think all these people will be on it?
I've never heard anything about birth control raising your cancer risk. I don't see why it would. You're giving yourself a form of estrogen and/or progesterone, not some sort of carcinogenic thing. If you're on something that's been around for 10+ years, you have even less reason to fear it causing cancer because it would have been pulled from the market if it was linked to cancer.
You could mistake an early miscarriage for a period even if you're NOT on birth control if you never had any idea you were pregnant, so it's really nothing to be concerned about. If you were to get pregnant on the birth control (usually because you're not taking it properly), you'd miss your period like anyone else.