Tradesmen own their tools.
A Trade is by definition, "An occupation, especially one requiring skilled labor; craft: the building trades, including carpentry, masonry, plumbing, and electrical installation." The skill labour requires the the Skill of using specialized tools in practice of the trade. As such, Tradesmen are expected and usually required to provide their own tools so they can practice their trade.
The Twitter account in question was being used by the journalist to practice his trade. IT had his name on it. (all of my tools have my id on them too).
It follows that the account was and is a specialized tool of the Skilled Trades Person employed to practice his trade and the tool goes with him when he goes to his next job, contract or appointment.
They should get over it.
The followers of the account were following the author not the company.
Even Hair Dressers have "followers" who will follow them to the next Salon. Nothing the company can do about it. The followers don't belong to either.