This is an anomaly in the way the site works, all the Northamptonshire villages listed are in the postal town of Peterborough as they have a Peterborough post code and so get listed in there and appear on the Cambridgeshire page. If you look at the Peterborough page
here it says "Areas in the postal town of Peterborough". Likewise the Royal Oak has a Stamford post code (PE9) and gets listed in that postal town and therefore Lincolnshire. They should also really appear at the bottom of the county page where it says "Areas also in Northamptonshire", not sure why they don't, there must be a glitch in the code and that's one for Dave.
This pub shows what usually happens, on the pub page it says North Yorkshire / Otley / Blubberhouses but appears on the
West Yorkshire / Otley postal area page as it has a LS21 post code and at the bottom of the
North Yorkshire page under "Areas also in North Yorkshire", there are a few more pubs near county borders that appear the same way in their postal town regardless of county and on the "correct" county page as "areas also in...".
One last point is that the county does not appear in the pub addresses.