Ethanol is metabolized to acetaldehyde, which will make you feel bad. Taking a drug that inhibits metabolism of acetaldehyde to acetate (e.g. disulfiram/Antabuse) will exacerbate the hangover. I can’t say whether minor components also contribute but you can get a hangover from the purest ethanol.
That’s likely what happened here.
While it’s true that there are lots of risks in illegal distillation, the biggest risk by far is in illegal distribution. Moonshine can’t legally be sold in a liquor store. It ends up in nip joints and shot houses and speakeasies and so forth.
Every step in the distribution chain is an opportunity for someone to maximize their profits by adding adulterants. The safest adulterant is of course water, but customers would detect a weakened product, so the adulterant should have a sensory “kick” (but again, without the flavor being off too much). So that steers distributors toward commercially/industrially available solvents, ideally alcohols.
Moonshine is an illegal drug. Illegal drug distributors adulterate their product because consumers have no recourse. It’s that simple.
From my understanding, you have to try pretty hard to make moonshine with enough methanol to kill you (like you would have to deliberately concentrate the heads and tails of the distillate). I’m betting that it’s ethyl alcohol cut with methanol.
(Ah, actually, I see that what you say does not necessarily contradict the above.)