Actually I believe the battery is the phone companies responsibility, because it is their responsibility to ensure phone service remains during a power outage, just as it is with POTS. The fact that the power is now supplied via CPE rather than down the copper line from CO does not change that.
If they refuse to replace it. Complain to your PUC and your State Attorney General.
Obviously you dont realize that the majority of FiOS customers are now classified as DIGITAL VOICE. A few still are categorized as POTS/regulated over FiOS, then you can complain, but keeping it that way for the sole cost of a battery is absurd.
If you believe that Digital Voice should be regulated, then all the cable co phone, Vonage, even magic jack should all supply BBUs as well. Little hint, the Verizon ONT is technically their cable modem.