If Stalin was "helped" to the grave, the "last straw" was probably the "Doctors' Plot" allegations he engineered beginning ca. January 1953, supposedly "unmasking" the plans of some Kremlin doctors (curiously, all of whom were Jewish) to assassinate various Soviet leaders at the behest of western intelligence services. There is evidence that Stalin planned a simultaneous removal of Soviet Jews to the new "Jewish homeland" of "Birobidzhan" in the Soviet Far East, in the remotest place in the world, where they could be murdered out of the sight of prying eyes. (See, "Stalin Against the Jews," by Arkady Vaksberg, published ca. 1994).
BTW, "folk singer," Clinton Administration honoree, and unrepentant communist Pete Seeger wrote a little "folksong" at the time about what a great place this "Birobidzhan" was, bless his little heart...The chorus went: " 'Dzhan! 'Dzhan! Birobidzhan! Gonna pack my stuff, goin' to a new land!" (Can't you just hear him playing that on his banjo...?)
That's why I don't have the least bit of trouble believing Stalin did a crazy-@$$ed thing like ordering John Wayne's death. :)