Nothing to prevent a mother registering child and providing whatever details she wished to but it makes little difference. Anything can be written on a certificate but that doesn't mean it is correct, the DNA wins every time. My grandmother registered 16 children though 4 were abandoned between 1918 and 1928 within a month of the registrations taking place. Some of her descendants refuse to accept their DNA results as they contradict the paper trail, a few 'we're not related' comments have been made over the years, some via comments in public trees, to people they share 350-400cM with, I sometimes wonder how different it would all be if the certs didn't exist.