Yes, certainly funding has an impact on journalists' independence. That's why one of the most important principles is to have a pluralistic array of funding, so that news organizations are not dependent on any one company, one government or one revenue stream. Ideally, you would see an array of mainly advertising-supported funding.
Also, I think there is a role for tax benefits or taxation of the tech platforms, to ensure that they are compensating for use of this data by creating subsidies or incentive programs.
If you have a lot of different sources of funding, then the power of any one source to—