And considering serum cholesterol cannot pass the blood brain barrier and that it is all synthesized de novo in the brain makes it an even sillier claim. Your serum cholesterol level does not have impact on your brain's cholesterol levels.
Quite a few organs have the ability to synthesize cholesterol as needed and can do so just fine. Another area where we make use of cholesterol is for synthesizing hormones... but those organs can all synthesize it de novo just fine too.
The new pkcs9 inhibitors have gotten people down to extremely low levels of LDL (<30 and <10!) and found no impact to cognition, hormone production, etc. We have mendelian randomization studies looking at people that genetically do not produce pkcs9 and have basically nonexistent serum levels of LDL, no impact to cognition, hormone production, etc.
https://pubmed.ncbi.nlm.nih.gov/36779348/
https://www.ahajournals.org/doi/10.1161/ATV.0000000000000164
https://www.acc.org/Latest-in-Cardiology/Clinical-Trials/201...
https://www.acc.org/Latest-in-Cardiology/Clinical-Trials/201...