Although there may be no way to prove this, unsavoury things did happen in those days. One of which was actually purchasing boys for work, thereby relieving the parents of their obligation and providing a ready cheap workforce for the purchaser. Of course this was illegal even then, but it did happen and lots of records could be very easily altered. One did not have to provide proof of identity when notifying a birth or death, just rock up say who you wanted to be and get the record done. This occurred with Births and deaths, only thing was the dad could not be named at a birth if he wasn't at the record office.
The family doesn't seem to be at the very top of the law abiding citizens group and may have been a little loose with the truth and a little to easily swayed to the wrong side of the tracks when it came to upholding the law.

Not passing judgement just being the devils advocate.

Neil
