BF4 servers we all play on are paid for by someone - an organized clan or community, friends, or individual folk(s). Paying for and providing a server means they can utilize many set ups, protections (EB, DICE, PB, PBBans, GGC, ACI) and rules to ensure fair and honest game play for everyone if that's what the payee wants. That's THEIR choice! Most of them DON'T want cheaters! That's THEIR choice!
EB may issue a global ban or a 2 minute kick. The payee decides (via streaming to third-party anti-cheat sites PBBans / GGC / ACI) if they want that 2 minute kick to result in a ban.
If EB determines a false positive, the third-party anti-cheat sites will remove the ban from their MBI. Only time will tell. As it is now, "We do not find this violation to be triggered in error, and it will not be removed."