What's the "phone company" though these days? AT&T, Verizon, etc. provide little local phone service, although I guess that have to maintain the old infrastructure. I think most "landlines" these days are VoIP that won't work without internet access. I remember when my parents decided to get VoIP, it became a chicken or the egg problem because that automatically cancelled their DSL. There was some discussion of whether or not AT&T could connect a "dry line to restart their DSL service". They ended up getting AT&T U-Verse internet. I don't believe these new services are regulated quite like local phone lines were.
I guess it really depends on what kind of battery backups are used. A lot of these newer fiber optic networks are a series of transmitters that have to retransmit, although they should be quite efficient.