I think we could find we have overstretched ourselves if we become too prescriptive and the end result will be that we drive people away. Whilst many places will need a country to be comprehensible, there are others, London, New York, Paris and most US states which stand on their own two feet. Whilst it is desirable to include a country, any system must be able to pick out major cities etc. as well as a country. Perhaps we need a system that is able to highlight profiles which have one location in common be it town, city, county, state, country. That hopefully would sort out your William Jones born in Wales, Utah or Timbuktu.
I would go on to add that we do need to pare down the number of matches where the name is nothing like that input, so perhaps the system needs to work on a maximum of one letter different which would sort out some less than appropriate suggestions.
No system will ever be perfect so maybe we just have to try to design one which picks out 99% of the potential matches.