Sure, technically you can get a battery from whomever you like for your car so long as it's compatible - but the Manufacturer has put DRM on the battery interface. All in the name of safety, you see - they don't want to see their cars catching fire on national news because of some shoddy batteries.
However what it'll mean is that unless the battery maker is willing to fork out a large chunk of cash per battery to the car maker, the car maker won't certify it as compatible.