That's not a false attribution or nuanced, it's exactly what it sounds like from the short version lol. The German could even be translated both ways.
I disagree. Marxists use their dodgy paraphrase to paint religion as a drug of dependence peddled by priests. Marx actually wrote of it as a painkiller used by the oppressed. There is quite a difference. Marx himself was quite conflicted about religion. He came from an observant Jewish family, and despite his professed atheism, religious themes reappear in his works.
Those two are the exact same thing.
The dodgy misquote, in a modern context, casts religion by analogy as a social blight, entirely negative, with an implied solution of organised state violence. The original casts religion as something positive that makes life bearable for the masses in a fallen world of bureaucracy and exploitation. By implication, religiosity is humanity's second best option. Best option being Revolution. Of course. This is Marx.