If you claim, for example, that an input is not stored, but examples of internal steps of an inference run _is_ retained, then this paper may suggest a means for recovering the input prompt.
Here's an output text: "Yes." Recover the exact input that led to it. (you can't, because the hidden state is already irreversibly collapsed during the sampling of each token)
The paper doesn't claim this to be possible either, they prove the reversibility of the mapping between the input and the hidden state, not the output text. Or rather "near-reversibility", i.e. collisions are technically possible but they have to be very precisely engineered during the model training and don't normally happen.
Surely that's a stretch... Typically, the only thing that leaves a transformer is its output text, which cannot be used to recover the input.