This simple fact is the greatest argument for distillation having much higher legal barriers than the simple brewing involved in beer/wine/mead.
Poking around the web, it seems as if making liquor at home has become popular among booze nerds. That's great and all, but I wouldn't call it moonshine, and I'd be very hesitant about how much I reasoned based on what well-informed people do today about the practices of a century ago, or indeed about the practices of today among those for whom making moonshine is more a family tradition than a hobby.
The vast majority of moonshine stills were just churning out unaged corn whiskey from animal feed corn. There is no risk of methanol poisoning in that scenario.
So why was methanol poisoning common during the Prohibition? Renatured fuel alcohol. To stop people from drinking fuel ethanol, the government poisoned the supply with methanol. People tried to come up with jerry-rigged solutions to remove the methanol, and more often than not failed. Some less scrupulous experimenters sold their results anyway, where it worked its way into the black market supply chain.