The situation is not so clear with Apple (but there is some evidence that it puts up at least some opposition: see hit-pieces like https://news.ycombinator.com/item?id=27968394 and note all the pro-Chrome/Google opinions there...) but Mozilla is funded by Google.

...and regardless of whether you're using Chrome, the immense power of Google's marketing abilities cannot be overstated. It is an ad company, after all. (If you're using Chrome, it's self-explanatory; if you're not, you should notice just how much you get "recommended" to.)