I work in Quality Control for artisan distillers - heads and tails recycling is an important part of the production process, and requires both skill and testing to make sure methanol is removed from the spirit.
A bootlegger would need 1) a fractional still or 2) precise temperature control and monitoring - they were unlikely to have either.
Furthermore, I find it doubtful that an illegal bootlegger would have used pure sugar for their mash - that would have been far more expensive than the purchase of grain.
Finally, on point 1, the foresight and knowledge to remove methanol doesn't come in a nice pamphlet with the illegal still - we know that a lot of the alcohol produced by the illegal bootleggers (who the government did not have control over) was contaminated with methanol (And other heavy metals or contaminants).
On point 3; Sure... that's almost right...
Industrial alcohol not made for human consumption would already contain methanol and other contaminants; the law establishing a minimum level of contaminants to render it undrinkable by humans did theoretically make it more harmful.
That does not constitute a "Federal Poisoning Program". - when someone hears those words, they don't think "the government established that already undrinkable industrial alcohol must contain a minimum level of naturally occurring contaminants to stop individuals from consuming it";
they think "the government purposely added poison to alcohol sold to individuals for consumption" - which is not what happened.