All this aside, the argument being framed this way in the first place is strange. Why do they place so much weight on the personal relationship between these two men?

Besides Great Man shit and monarchist brain, I think a lot of the history of anti-"Stalinism" rhetoric, especially but not exclusively in "left" spaces in the west, can be traced back to Trotsky, who loved this shit, and then his acolytes, who arguably loved it even more, before filtering down to anti-Marxist "leftists" like Orwell, who can be very plainly seen to have absorbed Trotskyist historiography even if he was not himself a trot (see the characters of Goldstein and Snowball and how the evil bureaucrats hate them so much), and then saturating all western discourse about communism that isn't just 20 trillion dead vuvuzela iphone.

That and people in our society are really strongly inclined toward black and white views of the world, so if they want to acknowledge that Lenin did a lot of great things then that requires making him not literally immaculate but highly sanitized and to have had his work corrupted by the Bolshevik Cain (I believe that's the title Trotsky gave Stalin in at least one of his little essays, but some later trots made him more like the Devil of Communism who blasphemed against the Heavenly Father Lenin and murdered the Heavenly Father's Son, Trotsky, and is now responsible for every ill related the Marxism). I still don't really understand why this subset overgeneralizes like that, but I've had Trots explain to me that their ideology is literally defined against Stalin, and I agree with them, so perhaps it's to try to have the greatest level of salience possible by making all the actual/nominal communists they hate from Mao to the late USSR be representatives of Stalinism (yes, I've seen both claims made emphatically). That's just a guess, though.