There's more than 200 countries listed on https://en.wikipedia.org/wiki/List_of_sovereign_states (I didn't actually count them, but jQuery says the table has 238 rows; a few of these are headers/footers, but there's still enough to have more than 207.) That isn't exactly equal to a nationality, but it's probably a good minimum - I could easily believe that there are more than 207 nationalities.

the un has 193 members and there are still 54 countries that aren't a member of the un, so, it might be possible that they have that many nationalities, but I doubt that this is untrue.