The account, called ElonJet, is still suspended. Jack Sweeney, the account's owner, used publicly available flight- tracking information to post every time Mr Musk's jet takes off and lands.
The account was blamed for an incident in which Mr Musk's son was accosted by a crazy stalker.
Mr Musk said legal action would be taken against Mr Sweeney.
Users may not publish or post other people's private information without their permission, according to the updated privacy policy.
The journalists were suspended for reporting on the jet tracking account incident.
Governments and journalists condemned the move after the suspension.
Fleming said that media freedom is not a toy. The cornerstone of democratic societies is a free press.
The Digital Services Act requires the respect of media freedom and fundament rights, which is why the EU commissioner threatened to impose sanctions on the social networking site.
Mr Musk has made a number of changes to its moderation practices since he took over.
He has restored a number of previously banned accounts, including former President Donald Trump's profile.
According to the New York Times, the CEO of the electric car maker slashed the staff of the social media company and stopped paying rent for some of its offices.