Surely that depends on why she was sacked.
When you announce a sacking publicly people are going to speculate.
If you then shut down and say nothing that speculation grows. We’ve already had people speculating about why SM might have been fired, based on previous conducts of other BBC personalities.
Not at least giving some indication in this instance could lead to far more damage to the individual if that’s not the reason than if they at least give some indication as to what it was about.
Let’s not pretend that the vast majority won’t have jumped to a certain conclusion here.