Why Is Google Funding Its Own Competition In The Firefox OS?
forbes.com
forbes.com
What this means is that they don't give a (large) hoot if the eyeballs are looking through Firefox or Chrome (to elaborate a bit, I imagine Google would prefer if the eyeballs came through Chrome, but Firefox eyeballs still pay the rent). So from a purely business standpoint, I suspect the "loss" of promoting Firefox OS is less than the "loss" of not being Firefox's default search engine.
Also, competition is, as far as I understand it, to Google, A Good Thing. There are probably lots of reasons for this, at least one of which likely has to do with how the Microsoft antitrust thing went down back in the 90s.
Mozilla makes money off Google. Google does not hold the purse strings and therefore cannot tell Mozilla what to build and what not to build. Of course a business deal could be made that restricted Mozilla's options, but I'm not aware of any such restriction and I don't think the non-profit organization would ever accept such an offer.
There are other incorrect assumptions in the article, which are not backed up by fact or interview sources.