Board Game Arena

Why does BGA occasionally give the error message ”you are playing from the same location as player [name]”, even though those players are in a different country than me?

Because you are (or have been) on the same IP address as them. That's the only thing they have to go on.

Do you use a VPN?

How do you know they "are in a different country"? If you go by their flag, that's a something selected/chosen by the user and does not necessarily have any relation to the actual location of the user.