A tweet is a privately published message, not one put out by the Sunday Times or Penguin Books.
It reflects badly on the person, and not on an employer, that most people will not even make the connection.
I confess that I have never heard of Indian Knight and did not know who employed her until I looked it up.
While I believe that people should face the consequences of stupid things they write on Twitter, losing their livelihoods for an off message tweet is going too far.