I think the main point they’re disagreeing with is this:

you wouldn’t be able to mathematically prove that the signal is perfectly recovered 100% of the time for all possible inputs

They explain why you don’t need 100% accuracy - most compression codecs would only use the network for a prediction, which doesn’t actually have to be correct. It just has to be “more likely to be correct” than existing algorithms.

If you want to read up more on the context of these prediction functions, the general class of compression algorithms you’d use for this are called prediction wavelet codecs. FLAC and arguably PNG are both prediction wavelet codecs.

Someone shouldn’t say that mounting climbing should be banned for only a few deaths here and there, when you have literally any other sport causing more harm.

I’m all for keeping mountain climbing legal, but I don’t think the logic behind this holds up.

Russian Roulette has a far higher rate of death in participants than fishing, but probably results in less yearly deaths. By this logic, Russian Roulette should be legal because it causes less overall harm.

Applying the same logic to your animal example - I found a study saying tigers kill on average 1-2 people in the US per year, less than 1/10th the number killed by cows. Does that mean people should be allowed to own tigers?