Admiral Kirk would be the commanding officer and thus the one that would attract the attention of the media. What happened to Captain Decker might never have come out in public. He and Illia are MIA.
I would think some of Kirk's missions and encounters during his time as captain of the Enterprise, and perhaps before that, would have been noted in the media. Especially anything that could easily be made public knowledge. The incident on Station K7 could easily be made public. The disaster at Cestus III with the Gorn, or Deneva with the parasites would have gotten into papers after the loss of a major colony. News about the Romulans returning many have gotten into the news, and Kirk's role in keeping them away may have been mentioned. The Babel Conference may have been news worthy. Some incidents with the loss of a major starship may have also made the news. The loss of Defiant, Constellation and Intrepid. The deaths of the crews of Exeter and Excaliber. Probably the incident at Organia that ending the short war with the Klingons was something news worthy.
I would think some of Kirk's missions and encounters during his time as captain of the Enterprise, and perhaps before that, would have been noted in the media. Especially anything that could easily be made public knowledge. The incident on Station K7 could easily be made public. The disaster at Cestus III with the Gorn, or Deneva with the parasites would have gotten into papers after the loss of a major colony. News about the Romulans returning many have gotten into the news, and Kirk's role in keeping them away may have been mentioned. The Babel Conference may have been news worthy. Some incidents with the loss of a major starship may have also made the news. The loss of Defiant, Constellation and Intrepid. The deaths of the crews of Exeter and Excaliber. Probably the incident at Organia that ending the short war with the Klingons was something news worthy.