There's nothing in general about a tweet that makes it any more or less legally binding than any other public communication, and they certainly can be used in legally binding ways. But sure, a simple assertion to the public from the CEO of a privately held company about what a separate contract says is not legally binding - whether through tweet, blog, press release, news interview, or any other method.
e.g. google project maven, microsoft hololens (military), and much much more
Okay, yes, if you openly and directly state a unilateral contract offer and you're already in trouble with the SEC, Tweets can be legally binding.