Apparently, Verizon really takes their disclaimers very seriously, and reality is secondary. Watching the new Verizon Samsung Galaxy S III commercial above, you could be forgiven for mistaking it for a Galaxy Nexus instead. Check out the mixture of on-screen function keys just like those on the Nexus, at about the 17 second mark.
Also, from all the industry intel we have heard, the SGS3 will not have carrier branding on the front of the phone, just on the back, yet in the video the Verizon logo is right there on the front. Of course, it's Verizon's commercial, so they can do whatever they want with it, even if they did take some "poetic license" with reality.