I think it's a variant of the latter -- IIUC no information can be "lost" in reversible computing, so the output of a reversible hash function might be both the hash and some number of other outputs, all of which you would have to know if you wanted to reverse the hash function.
It seems there is an analogy to be drawn to the way in which there can be no "waste heat" in a reversible thermodynamic process [1]. I thought this analogy might be a bit of a stretch at first, but looking into this a bit more it seems as though this is indeed exactly the idea with reversible computing, such that if a reversible computer could be implemented at the hardware level there would supposedly be significant energy efficiency gains on the table [2-4].