Journalists have an obligation to protect their sources, which prevents many stories from being independently verified. However they can be verified by other news outlets, who have their own sources. The "losers and suckers" story was independently verified by NYT, WaPo, and AP. But the NYPost has not been verified by anyone, nor they did seek verification, nor did they even ask Biden for comment, because they know the story is bullshit.
The "double standard" idea makes my blood boil, because it casts basic facts in partisan terms. Twitter fact-checked Trump tweets, but not Biden tweets. But that's not a double standard; it's a single standard, and it just so happens that Biden does not tweet outright lies such as "California sends a ballot to anyone living in the state."
Twitter clearly does not want to be in this position and the right-wing misinformation machine is exploiting that aggressively. The NYPost story got a huge Streisand-effect boost. It's impossible to give Twitter good advice today.