For example, it's definitely false to claim that Donald Trump won the popular vote yet there are a multitude of fake stories on FB that claim as much.
People shouldn't be silenced just because you disagree with them. Many disagreements come down to a different evaluation of "the facts", some element that the one side would say the other side has objectively incorrect. Both sides have the same data, but they have a different interpretation about what's an "objective fact". It is critical that we allow those discussions to play out.
Platform owners becoming the fire companies of Fahrenheit 451 is a dystopian horror show. It cannot be emphasized too strongly that users MUST be allowed to choose for themselves and have free range over the marketplace of ideas.
GP says that facts that are false (namely, Trump won the popular vote) made it onto the newsfeed.
You said that there is a "different evaluation of the facts". The popular vote count is a number. How, pray tell, do you disagree with a number?
First, the entire popular vote has not yet returned. Several states are sitting at 99% reporting, and Utah is sitting at 94% according to NYT. You can say that most of those votes are probable Clinton votes, but the simple fact is that the count isn't finished. The popular vote will continue to change until all the votes have been counted. "It ain't over until the fat lady sings". A Trump supporter could easily make this argument and have the "objective fact" that we don't know the final popular vote tally on their side. You must now convince them that this hard reality is either not so real or not so important.
Second, there are people that believe either faulty or intentionally modified equipment caused many people to vote for Clinton unwillingly. For example, there's a video of a voter unable to select Trump on his electronic ballot; the touches repeatedly register as Clinton though his finger is clearly pressing the Trump option.
That's one anecdote, but a Trump supporter who wants to claim the popular vote could say the election was rigged in Clinton's favor and that while the official numbers show more Clinton votes, the true numbers (which are impossible to measure), i.e., the number of voters that actually wanted Trump to be president, were larger than the number of voters that actually wanted Clinton to be president. The supporter could use a collection of anecdotes similar to the one described above as supporting evidence. They could also use the recording of HRC expressing interest in rigging the Palestinian election as supporting evidence. No "hard numbers" here, but some objective facts that could be used to cast doubt on some of the hard numbers.
Thus, "objective facts" and "hard numbers" become more ambiguous because the other side doesn't believe the entity that is issuing your "objective facts" is credible. You must first convince your opponent that the machines were not altered (which is not possible to prove), that any official tampering with the vote counts was insufficient to push Clinton over the top (also not possible to prove), and that there is an insufficient quantity of votes outstanding to result in a Trump win (possible).
This same thing happens whenever a research study is released. If the audience approves of the study's findings, they say "Yes, this is an objective and good study." If the audience disapproves of the study's findings, they say "This study cannot be trusted because its author holds political views X, Y, and Z, the institution's primary donor is a company that stands to make money from these unpopular findings, the methodology was incorrect because the sample was too small or too large and the control group was not adequately controlled". These are debatable, subjective elements of study design that can't be objectively proven or disproven, and they can be used to cast doubt on any "hard" source you want.
The fact of the matter is that humans are excellent at retroactively rationalizing at least semi-defensible arguments against someone's "objective facts". Every side seems to believe all of the "objective facts" are in their favor. That should tell you that "objective facts" are worth practically nothing when it comes to human decision making.