I can't imagine that any regulator would have a problem with a company tightening up any guidance/direction contained within the RFM.
In the case of the quoted battery over-temperature, for instance, if a company wish the pilot response to be 'land as soon as possible' rather than 'continue flight' then that's fine, but if they changed a 'land as soon as possible' from the RFM into a 'continue flight' in their company drills then that's a entirely different matter which I suggest would not stand up to external scrutiny in the same way.