Yes, it does look there has been some 'interpretation' :-)
I think I'd first try to find out if they were married in a church in Bedlington (the service record doesn't say if it was a church or a registrar office wedding). A copy of a church marriage register, if it exists, is lots cheaper than a cert and has the original signatures which is far nicer.
If she died in Scotland, the death cert should give name and occupation of her deceased husband plus both parents' names so may be just as good, if not better, to confirm it - with the usual caveat of 'as far as the informant knew'
Boo
I think the tree owner may have interpreted the place they married (ie) Bedlington as her birthplace
Still a good idea to get the 1913 marriage cert