The reason they denature alcohol is so people won't drink it. The only alcohol that is denatured is ethanol, which is drinking alcohol - or the stuff that makes you drunk. The reason its denatured is because it's used OTC for medical use and not regulated and taxed.
They can add any toxic substance to it to denature it, and you have "denatured alcohol". Methanol (wood alcohol) isn't easily available OTC - just isopropyl and ethanol. However, they could be adding a small amount of that as the denaturing agent.
But honestly, I think they mostly add a bit of isopropyl in most OTC ethanol.