Its quite possible that Mary Ann was actually not born in Rivington. There are 3 scenarios that I can think of.
1 - she says she was born there because that is what she was told
2 - she assumes she was born there because most of her siblings were born there
3 - her employer (if she was working) filled out the papers and assumed she was born there.
You might need to start looking at other parishes. First check which parish the mother came from and check the OPRS for that parish first.
I have the same thing with one of my families. The siblings were all born in Somerset but grew up in Devon. On the census records some of them say they were born in Somerset and are consistent (and quite correct) about it.
At least two members of the family kept changing their minds so sometimes the census record says that they were born in Devon and sometimes they were born in Somerset.
At least I know the OPRs in Somerset proves that they were born in Somerset.

Hope this helps.
Burrow Digger