Just to clarify - how you get a replacement phone depends on the circumstances. If the issue that arises is damage or loss, then the insurance (Asurion or other) covers it (as long as you bought it, you have not used it too many times, and don't fit under their exclusions) and you deal with the insurance carrier, not Verizon. In cases like the OP has, which is clearly a warranty issue, you take it to Verizon, not the manufacturer. You probably can deal with the manufacturer, but as the OP noted you will be without a phone a while. There may be some gray areas where Verizon will need to decide what is covered under warranty, what is damage, what may not be a problem, and what may be tampering which is not covered at all.
A day after I posted my original message, the problem with my phone disappeared. The back light is now functional and everything seems to be good. As far as what I am leaving out, not sure what you are getting at? The phone has no physical damage and I am only telling you what I was told from Motorola Support. I never thought to go through Verizon because I was under impression that the warranty with them is only 30 days. If I can bring this phone to a Verizon store to get swapped, then I will obviously do that. Would hate for this to happen again.