In advance, thank you for educating me.
Painkillers, caffine, LSD, and other psychoactive drugs all cross this barrier by definition. In terms of damage, there are many possible mechanisms once in the actual brain tissue. Quite often drugs would act on a receptor on a cell, which would change how the cell operates in some way, such as by inhibiting an ion channel.
increased blood pressure leading to a stroke localised inflammation of brain tissue (which can be caused by an autoimmune response) oxygen deprivation enzyme degradation, where an external chemical blocks some of the chemical processes that keep brain cells working (drinking mercury will do this)
The second one seems to have happened here. The may have drug triggered a wildly excessive autoimmune response called a cytokine storm, which is the immune system's equivalent of a firework display where everything is launched at the same time. This basically poisons you from the inside in various colourful and unpleasant ways.
There's nothing about oral ingestion that makes it more or less likely to cause brain damage. Many chemicals can survive stomach acid and pass into the blood stream. The drug on trial was one of them.
Layman translation: Methanol is transformed into Formate, that is another substance. Formate mess with the functions of the mitochondria, that are the parts of the cells that use the oxygen. So each cell dies like it would die if you can't breath oxygen.
(I suppose that the neurons are more sensible, and the visual problems are easier to spot, so one of the first symptoms of Methanol poisoning is blindness.)