While you do not have a legal duty to secure classified information it is illegal for you to possess it. It is illegal for a reporter to have and discuss classified information under strict interpretation of the espionage act, however the supreme court ruled that they can as long as they didn't participate in acquiring it or induce someone to acquire it. They will prosecute a reporter if they have a clear indication they participated in the theft of the classified information.

Regarding Gellman, he could have been prosecuted. Under strict interpretation he admitted to retaining classified information. The government is then in a catch 22 situation where they have to verify, publicly, the information he held creating a Snowden like situation where it is no longer secret. It is a very messy area of law and a zealous DOJ can exert tremendous pressure on individual journalists even though they are better shielded than non-journalists. Essentially, by prosecuting someone they have to prove it is national defense information and in so doing they will end up disclosing the information themselves making it dubious a jury would ever convict.

It is the same reason we can freely discuss Snowden-leaked information now. It is not a secret. Even if it is classified it has lost its legal protection.

In short, if this journalist even vaguely induced anyone to leak information to her she can be prosecuted and the precedent there is much less in her favor.