This is in general good advice, but in the context of healing the liver plants are generally the type of poison your liver exists to filter in the first place, so a meat heavy diet is likely better. Of course you are trading longer term cardiovascular health for short term liver healing so don't do this for long, but if your liver is very damaged avoid plants as well for a short term.
Enterohepatic Recirculation is heavily influenced by diet which is why fiber and specifically leafy greens seem to be helpful for liver heath. https://en.wikipedia.org/wiki/Enterohepatic_circulation
This is also one of the reasons activated charcoal is useful after ingesting a wide range of harmful substances.
I don't see the connection to what you wrote before it; would you mind to explain?
Unfortunately there can be a significant delay between ingesting the toxin and activated charcoal. However, substances can pass in both directions. So by lowering the concentration in the intestine it also increases the amount that diffuses back into the intestines after having entered the bloodstream.
But Wikipedia has a long article on Hepatotoxicity[0] and that suggests discontinuation of the drugs involved can allow the liver to heal (if discontinued early enough).
As a patient, you need to be conscious to ask questions and retain at least some control over your treatment whenever you can. If you're overwhelmed by what you are being told or concerned about the planned course of treatment, always ask questions, especially about long term implications and risks and how those are addressed. Generally doctors like being asked about medical things and are willing to answer when they are able. [Individual experiences may vary etc.]
Also, a few months later of taking this drug, my liver is perfectly healthy (results from around two weeks ago): https://i.imgur.com/WMpH4t9.png
That's quite an interesting molecule :)