Having it owned by a non-profit foundation would make a huge amount of sense, especially if that foundation was then immediately funded by a variety of companies rather than just one big advertising company.
The obvious test for whether the browser is actually independent: what is the response to "let's add an ad-blocker by default".
There would be few incentives to try and pull off something like that if nobody had any faith in the product every becoming extremely profitable though.
With Mozilla becoming so hostile to their power users in recent years (or any user who just wants to customize the interface or core functionality), I'm not sure it would make much difference.