You can absolutely get methanol from a bad batch of a fermented beverage. It's typically only a problem for distilled spirits because methanol's evaporation point is lower than ethanol, so you end up accidentally enriching your distillate; in non-distilled beverages there's enough ethanol to keep the methanol away from your liver enzymes.
That doesn't happen from fermenting. This might make botulism though
You can absolutely get methanol from a bad batch of a fermented beverage. It's typically only a problem for distilled spirits because methanol's evaporation point is lower than ethanol, so you end up accidentally enriching your distillate; in non-distilled beverages there's enough ethanol to keep the methanol away from your liver enzymes.