When Liverpool callled out dodgy VAR and talked about a replay they were mocked throughout the media.
It's also a pretty unique situation, with PGMoL admitting almost immediately that they'd made a total fuck up. Not any kind of subjective decision that people didn't agree with, but a genuine fuck up, where they'd made one decision, but passed on another. In those circumstances, I think it's fair that they released the audio to explain just how it could happen.
With Forest, they're just going to get the an "I don't see enough there", or "not enough to overturn", which is completely different level.