She might not have filled in the birth certificate but someone else (husband/partner/employer ?) remembering the Scotish connection or quite possibly confusing a Manx accent with a scots accent gave the wrong information - an easy mistake to make when you were not expecting to have to supply the information.

Re father - then burial record will probably be in parish in which body was found - if Douglas bay/harbour then very probably Braddan though Onchan is also a possibility