Power is not the issue, it is infrastructure: phone networks are not designed to be used at high usage rates (not too many people on at the same time), and that is the issue.
More than 2 million on both sides of the US-Mexico border without power - AP
I would guess over two thirds of the population only has cordless phones in their home and roughly about a third up too a half of the population in the city actually uses Cable TV phone service. IOW they can't talk right now anyway. No Power? No Cable. With a Ma Bell land line you will have service with cable you won't. With cells? Possibly either way.
The cell phones would put far more stress on infrastructure than land lines. Cells can not function without Ma Bells Land Lines. That's why his statement makes no sense.