The company should have had a long discussion with legal and posted a public statement. The CEO shouldn't have gone on his website and posted a comment as a response that sounds like a 5 year old having a temper tantrum.
"Whatever the employee may have done to deserve separation, it is profoundly weird and troubling (and also, implicitly threatening to all employees, whatever their rank or standing) to see a CEO discuss those reasons in public."
Going through legal and posting a public statement is still discussing those reasons in public under the psuedonym of the CEO with the words benig ghostwritten by legal.