Removing it from the normal tweet status is separate from preserving them. They could archive them and disable replies, retweets, quotes, and so on. They could remove it from feeds. They could frame it differently.
I know for a fact my aunt mails in ballots for her husband, her father and her mother. Claiming that there is no mail-in voter fraud among 300 million Americans is quite absurd in my opinion.
It's a bit absurd when claims of rampant mail-in voter fraud come without evidence from a New Yorker in the District of Columbia who votes in Florida by mail.
One, why haven't you reported your aunt for voter fraud? Voter fraud is a very serious issue and it seems to me that you're letting a criminal go free. This can be easily verified by telling the government and having the three others confirm who they voted for.
For two, if she is mailing in the ballots, then is she forging their signature as well as collecting their SSNs? Or are they simply signing on the ballots themselves agreeing to the votes? In which case is that truly fraud or not? If she's forging signatures then she's also committing identity theft which is a very serious issue, one that I hope you agree deserves reporting.
When you have become one of the de-facto news sources for a sizable portion of the population, it does sort of become your job.
Whether it’s good that they have become a news source or not is a valid question. But right now, they are, and I think preserving the president’s tweets seems like a pretty easily defensible decision. Even if it is also (or primarily) motivated by their own business interests.
Giving him a platform in the first place is what necessitates the consequent fact checking. If they didn't distribute his lies they wouldn't need to contradict them. Many media outlets have stopped airing Trump's statements live, because doing so is essentially unethical.