No one owns journalism. Even the media or the "big media" and the press do not own journalism. It is a practice that is not dependent on how it is being done since there are many ways of going about it. It is not the media, neither is it the press or any kind of state slash government property. Many would raise arguments here but journalism is ought not to be controlled or owned by anyone.
But one may notice the fact that the press and media do not own journalism rather they are interlinked with one another. Generally speaking, the information that the media passes on to the public comes from the process of journalism, e.g. reporting. Likewise, journalism is dependent on the media to pass on the information it gathers to the public or that information would just be uselessly lying written on pieces of papers or recorded on cassettes. The point here is that journalism is interlinked with media and press, not owned by them and all three are then dependent on one another in one way or the other.
Since society as a whole that consists of public, needs to know about what is going on around the globe, it is bound and dependent on the medium that provides it with the information it needs. Now this medium is controlled by the government for imparting news that the public needs to know and should know and controlling and holding back those news that won't harm or hurt the public it if doesn't find out. So when this medium is controlled and controlled here does mean ‘owned' when we talk about the government, the others that interrelated with the medium like press and journalism would eventually be controlled with it too.
These days, people who practice journalism do not want to be called professionals. I do not understand why this debate even started to begin with, because in my opinion, they are professionals. If a person likes to and writes stories or articles or whatever he likes and keeps them to himself, he is not a professional. But once this person starts getting his articles published or some pictures that he took while sightseeing in Switzerland get printed in The Sun newspaper's edition of country information for example, he becomes a professional. Logically, anything you write or any documentary you make and it reaches the public and influences their opinions to shift, makes you a professional. It could have been as simple as that.