There is a law, 18 USC 798, that punishes unauthorized disclosure of certain classified information. That is information which
at the time of a violation of this section, is, for reasons of
national security, specifically designated by a United States
Government Agency for limited or restricted dissemination or
The information must be actually, officially deemed to be classified. However, as cpast points out this is not applicable to all disclosures of classified information, and is only applicable to cryptographic or communication intelligence. So it depends on the nature of the information disclosed. Let us assume that the information disclosed is about the construction of the submarines. 18 USC 793 covers more general disclosures, but that offense relates to entering a protected facility for the purpose of harming the US. You have to start by reducing (a) which states the conditions defining the offense:
for the purpose of obtaining information respecting the national
defense with intent or reason to believe that the information is to be
used to the injury of the United States, or to the advantage of any
which means that you do the act in order to injure the US or aid a foreign country. Then, the act that is prohibited is when the person
goes upon, enters, flies over, or otherwise obtains information
concerning any vessel... connected with the national defense
Now the question is whether he entered a protected facility for the purpose of gathering information harmful to the defense interests of the US (contrary to the conditions of the security clearance). The hypothetical seems to say otherwise: he obtained some information in the course of his job, and some years later gained additional information indicating that the media lied. He is not guilty of violating 18 USC 793, because he did not enter a protected facility for the purpose of working against US defense interests.
Finally there is 50 USC 783. This prevents a government employee from revealing classified information
to any other person whom such officer or employee knows or has reason
to believe to be an agent or representative of any foreign government
where the information is classified. But in the scenario, the person revealing the information is no longer such an employee.
There is a time limit on federal prosecutions, and the clocks starts with when he discloses the information. Some crimes have no limit: death penalty offenses, terrorism offenses resulting in risk or actual occurrence of death or serious injury, child abduction and sex. The limitation is 20 years for major art theft, 10 years for many specified offenses, 8 years for assaults and terrorism offenses not involving death or serious injury, 7 years for hate crimes and major fraud against the US, 3 years for misuse of Treasury symbols and 5 years for "anything else". At most, and most probably, the limitation is 10 years, if you can identify an actual crime.
Legally speaking, there is no such thing as "sensitive military information". In fact, this was an essential finding of the Pentagon Papers affair, that it is not a crime to reveal sensitive military information, see this article from the Columbia Law Review.