I don’t think a foreign government or agency of one was a party to the assassination, because that seems … messy? But for that matter I don’t think it’s accurate to say “the government” or “the CIA” killed Kennedy. I think some extremely bad people did, with complex personal and political motivations.
It does seem possible that once the adults in the room realized what had happened they would have engaged their Soviet counterparts to assist with the clean up and avoid any dangerous misunderstandings, given Oswald’s background.
A lot of this has to do with how I think about “conspiracies,” essentially, that the larger the conspiracy needs to be, the less likely is. In my scenario above, only about 8-10 people would need to know what’s going to happen, and only 2-3 would really need to understand the moving parts. In other words, it’s less a conspiracy and more of a plan. The “conspiracy” in my scenario is the cover up after the fact, but that could have been accomplished with exactly the kind of official obscurity that the CIA under Dulles and and his lieutenants specialized in, led by Dulles and his lieutenants.