I disagree. I think the bigger the company, the more likely they less care about users/support/their image. They're 'too big to fall' and the sheep are already on the ship. I believe there's plenty of examples out there, I can give you two straight away [1], [2].
Google cares a lot about user privacy. If only a few percent of their users change their default search engine from Google to DuckDuckGo, they will loose a lot of revenue.
Well, seems like a few people are already looking around for an alternative [1] when it comes to privacy [2]. I can see some effort [3] but I'm not sure if addressing user's privacy concerns is their main goal.
[1] https://news.ycombinator.com/item?id=5523992
[2] https://news.ycombinator.com/item?id=12034608