Morley isn't, for me, saying that Putin's statement is a "nothing burger", something we can dismiss, a one day story. He says the statement shows "the relevance of the JFK story for todays world." If he believed the statement was nothing, that it was Putin only promoting his own interests (which it is, of course), then it would be just that, meaningless, of no consequence. But he's connecting the statement to the assassination (and the assassination to the statement) and from that arguing it shows the relevancy of the event for today, for us here now. It's not simply an event we can put alongside other major events like Pearl Harbor or 9/11. It's still with us (and not in Faulkner's sense of the "past isn't dead, it's not even past.")
Morley's trying again - as many Leftwing conspiracists (now joined with the MAGA Right like Luna et al.) have - to keep the assassination alive, to keep it in the news, to connect it to today. He's said numerous times that the country can't rest, can't move on, that American democracy can not be finished, until we uncover what happened. Oliver Stone has said this. Salandria, DiEugenio, others. It's why they obsess over it. I'll just note as an aside to Putin's statement that Morley's been, let's say, less than skeptical about Fabian Escalante's assassination claims over the years.
And for Morley and the others, what happened was "the CIA" killed JFK (for MAGA it was the "deep state"). And they - Angleton, Joannides, Harvey, the CIA villain du jour - need to be held accountable. Until that happens the assassination is, as Morley says with the Putin statement showing it, still relevant today.