The story was always that my two cousins were adopted and not related to each other even. People sometimes would ask them if they were twins. They would say "Nope, we're adopted."
Somehow it got out that their bio mom was their younger aunt. The older sister adopted and raised both girls as her own. Younger aunt/mom got married and started a family before all this came out too. It was a wild journey.
I have heard this is common in Catholic families. They hide the illegitimate pregnancy and someone in the family adopts the child or pretends it is an older married family member's child. This was in the early 80s so I guess it was possible to get away with it.