Didn't the government also add methanol to non-consumption alcohol products as well, contributing to those poisoning numbers?

This was likely the cause of the vast majority of methanol poisonings during the prohibition. You have to use exotic, hard to break down carbohydrates in your beer, wine, or mash (the pre-distillation fermented product), like tree bark, to end up with significant quantities of methanol.

Most of the methanol poisonings were from poorly "re"natured fuel alcohol.

Yeah, industrial alcohols were (and still are) "denatured" with additives to make them toxic or unpalatable and industrial alcohol was often used as a precursor for bootleg spirits during prohibition. I think modern denaturants lean more towards unpalatable than toxic.