I am told that, even though a new episode is not slated to show until it's usual weekly programmed time (ie. Power, airs 9:00 p.m. Sunday night), I can actually watch it before it airs at it's normal time. In essence, beginning 12:00 a.m. Sat/Sun. I can actually On Demand "Power" and see the newest episode before it actually airs at 9:00 p.m., Sunday night. Is this true? Thanks.
Would depend on the channel it airs on, but my experience is that channels show it on their regular channel first not on demand.
Some streaming services (not On Demand) run by content providers will make a show available at 12:00am on the day it airs. For instance, I know Starz will frequently do this with their original content.
As a FiOS subscriber, if you get a channel on your regular package, many providers will also give you free access to their streaming services and thus you can watch a show before it airs. If you have a device which has the streaming player for that provider and can display it on your TV (for instance, Roku has StarzPlay and HBOgo amongst many others), you can even watch it on your TV in full HD.
Power -- which is a Starz original series (I don't watch, but that's what Google says) -- I would expect would behave much the same as their other series on Starz (my wife watches Outlander all the time that way -- OK, maybe I do too).
That is most likely done by AMC not Verizon.