Under the Lanham Act, I think Sony has something of a case. Clearly damage was done to their brand. They will have no problem finding evidence of that with all the articles and forum posts that sprung up after the commercials aired.
Lambert, by holding a video-game controller, associates himself with video-game consoles. Can anyone deny that? Is there anyone who saw the advertisement and did not chuckle or point? Honestly? Then damage was done when the association was made.
I think the important part of the argument is going to be whether or not Wildcat Creek or Bridgestone knew what they were doing when they had Lambert playing a Wii and if it was an intended reference. If it was done to intentionally spice up the commercial then it's pretty obviously a "false or misleading statement". Personally, I have little doubt that Lambert, at least, knew what he was doing, and that Wildcat Creek was making a conscious joke at the expense of Lambert's previous employer.