But normal battlegrounds are region specific.

Every US server is in the same pool.
As is every EU server.

So if for example, Cenarius US (my original server) detests/reports boxers but Magtheridon US (my current server) tolerates/likes boxers... there's an equal chance of having players from either server in a non-rated battleground.

As far as I know, the only time battleground matters is for Arena and/or Rated Battlegrounds.