Do you have the images of the original entries for these two events? Back then the Anglican Parish Baptism registers were the only recognised 'proof of date and place of birth' which was important prior to civil registration as proving where you were born would be required if e.g. you needed to claim parish relief at a later date.
Not the same area but while transcribing Northumberland baptism registers I came across a good few entries recording that children of non conformists had been baptised in their chosen religion, and that had been recorded in the Anglican register at the request of their parents to show where they were born.
Maybe its that sort of scenario?
Boo