Have you or do you know anyone who has gotten pregnant within the 6 weeks after giving birth?

After giving birth we are instructed not to have any sort of penetration. But of course some women go against doctors orders and find themselves in a pickle.

I've read conflicting information about when a woman truly becomes fertile again after giving birth. I've read and heard differently that you aren't fertile until at least 4 weeks, when the lochia is gone, and I've heard that you are extremely fertile directly after giving birth.

Side question for comment, when does a woman truly become most fertile after giving birth?