It would appear that PunkBuster - the anti-cheat program - is banning innocent Battlefield players. The program, which runs alongside games such as EA's aforementioned shooter, is supposed to detect cheats and exploitative hacks, and then ban offending accounts.
EA acknowledged that the service currently has some issues, and offers some advice on how to resolve any issues being experienced.
The service isn't managed by EA (it's run by Even Balance), which means the publisher has no means of overturning wrongful decisions. PunkBuster bans are also blanket bans across all games that use the service, so an innocent player banned on Battlefield might then not be able to play on a variety of other titles.