If they had of chosen to play for Pakistan they would then be considered overseas players.
Plenty of instances of County ‘Kolpak’ players refusing to play international cricket so they can earn more as a Kolpak in County Cricket.
Could also be cricketers with Pakistani or Indian roots e.g Kabir Ali, Min Patel or Saj Mahmood.
Did they choose England, so as not to be considered an overseas player or were just not good enough for those sides and took the chance for international honours with England.
Or Boyd Rankin. Wouldn’t like to think it’s Ed Joyce.
Or what about Darren Pattinson the one test wonder who was an Aussie. His selection was controversial.
It’s says picked a handful of times but does that include Lions matches I wonder?