A service to the public needs to actually credibly serve the public. A bakery cannot refuse to cater a wedding, ever if they find the clients repulsive because they are two dudes, or whatever reason they have. Google should not be permitted to discriminate or censor search results, even if they find the clients repulsive because they are 4chan users, or whatever reason they have.
You're right, filtering results would be a concerning step. I guess this is why they've added a fact check tag rather than a filter. I think it's a good solution.
But then again, free speech doesn't mean you have the right to have your results shown on the first page of Google. If they change their algorithm to preference articles with fact checking, is it the same as someone refusing to make a wedding cake for two dudes?
They are totally at liberty to do whatever the hell they like, however much they want to portray themselves as non-evil and in the public interest.