It's pretty typical that what happens is the corporation gives some initial advice, and tries to find you good counsel. They basically have to get out, because the corporate employment lawyer does not work for the employee, and there is usually a clear conflict of interest between representing both employee and corporation interests at the same time.

Since Mozilla was not sued here, Mozilla may pay for his defense (depending on factors), but direct intervention usually does not happen.

The rest goes to your "public opinion" element. Mozilla may publicly support him, of course, but in most cases, associating yourself with a lawsuit is often lose lose, even in cases where it appears to be defending a good guy (Imagine if today they support him, and tomorrow it turns out he was lying).

They may just be hoping their name doesn't get dragged through the mud here. I haven't seen any public release from Opera accusing Mozilla of bad behavior, but if Mozilla comes out and says something very supportive, Opera may just do that. My guess is staying out of it publicly seems the best way to accomplish that.

It'll be interesting to see how this plays out.