Although rumors and accusations of police collaboration dogged Stalin for much of his early political career, these charges never really stuck onto Stalin. The tsarist secret police, the Okhrana, often employed a tactic of falsely accusing various revolutionaries of police collaboration to drive a wedge into groups that were already prone to political infighting. The underground nature of the Russian Social Democratic Labor Party's agitation meant that the daily activities of its various activists like Stalin are often quite murky and uncertain. Both activists and police often tried to get the better of the other in this context. The chronic disorganization and understaffed bureaucracy of the tsarist state added a further layer of confusion as it became much more difficult to prove or disprove collaboration.

In the case of Stalin, the idea he collaborated with the hated tsarist secret police became a political rumor too delicious not to perpetuate by his political enemies. But there is very little in Stalin's actions in the RSDLP that indicate he was playing both sides; he was quite committed to the cause of revolution. Although Lenin never particularly liked Stalin, he never doubted Stalin's commitment to the Bolshevik cause. Lenin's last testament, often touted as a Lenin's condemnation of Stalin's growing power, only singled out Stalin's rudeness and increasing bureaucratic power. Unlike other targets of the testament (the testament itself was quite catty to everyone, not just Stalin), Lenin never accused Stalin of being on the wrong political faction prior to 1917.

But the image of Stalin as an apolitical opportunist has a great deal of power for his enemies on both the left and the right. Left-wing Trotskyites favored this narrative because it meant that the greatest excesses of the USSR, which occurred under Stalin's watch, were not the fault of Marxist-Leninist ideology, but rather a deceitful demagogue. For the anti-communist right, Stalin's hypocrisy fed into larger notions of a fundamentally corrupt regime whose ideological pretenses of a Marxist utopia were just window-dressing for men's will to power.

Both these critiques of Stalin are somewhat silly not only for their lack of evidence, but also because a Stalin committed to the ideals of Marxist-Leninism is still culpable for the crimes and excesses of his rule. In short, Stalin does not need further charges, especially ones that are spurious and unsubstantiated, leveled against his character.

The bit about Stalin assassinating Lenin is definitely /r/badhistory material. Although Lenin's fatal stroke was complicated by an (attempted) assassin's bullet, the girl who fired it was from a rival Socialist party. It's a pretty long stretch to tie that to Stalin.