4.4.4.4 was what they originally wanted to set up DNS on (The guys behind 4.2.2.[1-6] that is ...) however those are not Verizon's or GTE's name servers, there is no resolver running on that IP address, it is on 4.2.2.2, and they are Level 3's name servers which they anycast for use on their network by their customers.
Using the DNS server is not suggested, since it is not officially a public DNS server, and Level 3 could cease the service at any time (in all likelihood that is very slim, since they have been telling their customers to use them for years now). Since they are anycast it will reach the closest server to your location when you query that DNS, and as such using it shouldn't be too big of a deal, whether you are a customer or not.
Please don't do this unless you're a GTE/Verizon customer. Use your ISP's or run a resolver yourself.