I think 'country' can mean 'village' only in some contexts (e.g. 'we went to the country' = «ми поїхали в село»), but not in this case: 'one country' is much more likely to be understood «одна країна» (i.e. 'one nation, one state') and not 'country as opposed to a city'.
In American English (I can't speak to British or other flavors of English) , country never means village. It is used to refer to everywhere outside of any city, town, or village.