I don’t think I can find many pressure groups that Mozilla supports that go against their values and in favour of Google’s, because the two are nearly indistinguishable. More than 90% of Mozilla’s revenue derives from search engine referrals. Either they do have a choice, and choose to stay with Google, or they don’t have a choice (as you suggest), and would lose almost all of their income if Google fails. Things that promote Google also promote Mozilla.

Flip the perspective around a little. Why do Google pay their nearest direct competitor in the downloaded browser market hundreds of millions of dollars a year, without even insisting on results in exchange for the payment?