I have never heard that.
When a woman takes regular birth control pills, she can have a period every month and not get pregnant, so I can't see why that wouldn't hold true for the mini-pill too.
I have heard of many women getting pregnant on the mini-pill though. The hormone level in your blood stream is almost nil 24 hrs after you take the pill. It's vital that you take the pill at the same time every day. Even being late taking the pill by a couple hours can result in a pregnancy.