I don't agree. Fusel alcohols may or may not be to blame. I think the major blame for a hangover is high sugar content, high tannin content and anything else that is going to pull water from your body. I can drink wine and not have a hangover and then triply distilled vodka and have a major one.
The MAJOR contributor to hangover is water retention and aldehydes. Aldehydes can't be avoided, as oxidizes to ethanal, or ethyl aldehyde.
As others have pointed out - taking antioxidants with water (vitamin B / C) before bed will remove hangovers. This is because they remove the oxidants - aldehydes.