Of course, the kneejerk reactions tackle this full on, but before I go, "Hurr hurr, why you so dumb, SONEE?" I'll say that it's more than likely that there may have been some kind of clause in Jerry Lambert's contract that stipulated that he could not promote any competitor's products, perhaps for a span of time (like a year or something).
The Bridgestone stuff was probably fine, up until it cross promoted with Nintendo.
I doubt they're trying to say that they own Lambert's likeness, more that they feel his inclusion in that promotional commercial for a Nintendo product violated their terms.
Who knows. Who cares. They'll sort it out in the end. If there is no merit to this case, it will be thrown out. If there is, well, then Bridgestone has already removed Lambert from the commercials.
Now: "Hurr hurr, why you so dumb, SONEE?!" Carry on.
EDIT: And as silly as it is, Jerry is recognizable as Kevin Butler, the VP of PlayStation commercials. In the public's eye, he is a face now attached to PlayStation. Seeing him promote Nintendo is jarring for a public that is accustomed to seeing him be promoting PlayStation. I think it's silly, but the public associates things in silly ways when it comes to what they see on TV.