I guess I kinda have one too, though I can't say it was with correct use of BC.
I'll just start by saying that I have endo which resulted in an ectopic pregnancy and the removal of one of my tubes. I was in High school then, with a different partner, and I was taking BCP, never missed any.
So I only have one tube. Fast forward, different guy, my husband actually. He's been on chemo since he was 14 yrs old. They told us he was probably sterile from it.
Low and behold, we got pregnant with my daughter within months of getting married (no birth control)
After I had my daughter I had an IUD put in. Fast forward to this new years. Our marriage had been on the rocks and I was actually getting ready to move out. We hadn't had sex in at least 6 months. Well, a couple weeks into december, my IUD had accidentally came out during a Diva cup misshap. It was quite painful, I'll add.
Anyway, about a week later was new yrs eve. I'll save you the story, but quite a few too many drinks later it was new yrs day, and I had no recollection of what had happened, but we woke up in bed (I had been sleeping on the couch for months)
I found it kinda odd that I woke up in bed, but just grumbled about how stupid I was and forgot about it.
About 2 1/2 months later after spending a week in bed sicker than a dog, I finally realized I was pregnant.
So no, I didn't have any birth control, but my IUD had JUST come out and we hadn't had sex in at LEAST 6 months. It really does only take one time
All this from a couple who supposedly should have fertility problems.