Verizon allows pass through to Open DNS across it's network. I imagine if too many subscribers start using Open DNS Verizon will block access, put a stop to it in order to hold sway over their captive audience.
Another, more expensive, alternative Open VPN is also available.
Since Verizon still allows pass through to Open DNS servers you don't have to apply those settings to your router. Instead, change the DNS settings for your digital devices (e.g. PC, laptop, notebook, PS3, etc.) and you will achieve the same result w/o interfearing with Verizon's host name resolution process.