I recently heard from an unreliable source that a certain Chasidic rabbi in my hometown claims that the entire oral Torah in its current written form (including the Bavli, the Yerushalmi, and all of the Torah she'b'al'peh that came later) was given at Har Sinai and passed down orally verbatim until it was finally written down.
I am pretty sure that the person who I heard this from is mistaken because I have never heard anybody make such a claim, but that's why I am asking here whether there is any group or authority who make this claim?