Twitter is merely labelling a tweet as being factually incorrect, it's not hiding the content.
I think it really depends on what you view twitter as. If it's a communications platform, like your phone, then yes 'merely labelling a tweet' is as troubling as your phone company deciding to shut your call off when you mention to a friend that you're going to vote for Biden. If Twitter is a publishing platform, then it certainly can expose its editorial bias, but one must really consider whether or not it should have to pay its writers.
I fail to see how those two are equivalent, shutting off would be removing the tweet, they did not do that. Labeling something is not equivalent to censuring the tweet or cutting off communication.
Warning users is similar to phones letting you know they think a caller is spam.
This is a device feature, not a company one (I think at least). Plus spam has a clear meaning of unwanted commercial messages. I still receive calls from political campaigns regularly, and I would hope my phone company did not take it upon themselves to stop that.