Surely that depends on whose tweets they are? If its Jeremy Konyndyk or Scott Gottlieb or such that's a pretty decent source. If it's a celebrity or political figure or some random person less so.
The setup of this whole thread is 'trustable data and scientific method'.
Also, please be aware that a name is often not enough to show that a source is relatively trustworthy, some credentials can help; this is a worldwide forum.