i am sure these both accounts (bf4 and bf3) are somehow linked to each other.

https://bf4db.com/player/929752758

and ..

http://battlelog.battlefield.com/bf4/en/user/noob-not-found/

https://www.pbbans.com/mbi-view-ban-294492.html

We don't ban for BF3 accounts.

BF3 bans can be used as supporting evidence, but are never the core reason for a ban here.