Why would the USSR assassinate a US president at all? Why would they risk war (and their recent backing down in the Cuban missile crisis shows they really didn't want war) for something that gives them no strategic gain against the US?
I agree with you completely: I don't think Russia tasked an unstable loner malcontent with knocking off JFK and possibly kickstarting WW3 in the process. Russia did not want that.
What I think the US government feared was a public perception that Russia (or Cuba, or whoever) might have been behind it.
That's when swathes of the public and various grandstanding politicians start rattling their sabers and thinking about war. Any official story besides "Oswald was a crazy lone gunman" would have looked awful for the US and increased the odds of war, a recurrence of McCarthyism, etc.
So I don't think the possibility of a second gunman was ever seriously entertained, even though there's some evidence for it.
