Had to throw in my two cents. Even if Verizon was capable and willing to provide warranty replacement phones on demand, you probably wouldn't want them to, because you'd both be frustrated.
You'd walk in first and they would probably want to pull up your account. Of course you don't have one. They would want to troubleshoot when it's connected to their network, not the network your currently using.
By design, all warranty replacements are processed and linked to customers and accounts and you are neither....Not a bad thing, just a fact of life. Assuming they could just put a hold on your credit card and mail the replacement, while waiting for the defective device, would you really want to go through the process of filing a dispute if they showed the device was never returned?
Carriers are not really setup to provide support to non-customers. I would imagine if you bought the device and it was truly deemed defective, Verizon would replace it if you were within their 14 day return period, similar to a Best Buy, Costco, or Walmart. However, as others have said, once you are outside that window, you'll likely be referred directly to the manufacturer--Motorola.
They may be kind enough to send you a replacement, while they wait for the return. However, I wouldn't expect it, as I have heard mixed results.. Still, if I had a truly defective device, I would rather deal directly with the company that made it and not the middle man.
Obviously, it is much easier if you have the luxury of having spare devices, but it's not realistic to expect that people will have a spare Nexus 6.
I bought one from TMO and one from Sprint, since both were offering ETF buyouts and different promotions. I wanted to shop around, knowing that my phone would be unlocked and able to be used anywhere.
I still have Sprint, but haven't had TMO for almost 6 months. There is no way I would go to them with any expectation for assistance if my Nexus 6 was defective. As others have said, buy from Google (the carrier you are using) or Motorola (the manufacturer)
However, in my mind, given equal pricing, I would always buy directly from the company that made it.