The BBC is in a difficult position given Baker's employment status, or more specifically, lack of it, and the private nature of the tweet.
The tweet was not done under the auspices of the BBC - assuming it was his own twitter account.
Baker is not a salaried employee, his programme will likely be made by a media company he owns which has a contract to provide the programme to the BBC.
He takes no issue with the term 'sacked', but strictly speaking the freelance contract with the media company has been terminated.
That's why the BBC statement was carefully worded : "Danny will no longer be presenting a programme for us."
It also paid tribute to him as a broadcaster because even gobby cockneys have rights and the BBC will have wanted to avoid any hint of trashing his reputation.