OP, I still don't understand how dealer can say the battery is not under warranty. It should last the 4 years, 80k original warranty you have.
Current Bimmer: '16 SO F80 (Eisenmann/AA,Eibach = Oem+)
Gone but never forgotten: '13 FO e92 M3, Swifts, volks/advan, Akra Evo, Kics R40
Past: Alpine white e46 323i, Jet Black e39 530, Saph Black e60 530, Space Grey N54 e92 335, Mineral White N55 e92 335