There's no real evidence to support that.
1) The biggest thing is that there is often little to no correlation between manufacturing and pricing. Liquor prices are completely artificial, especially with high end liquors like Grey Goose and Patron that are just garden variety cheap crap with really great marketing. The ingredients and manufacturing process in that stuff is no better (and often worse) than the ingredients and manufacturing used in brands that cost 1/5th the price. Super-premium liquors, especially super-premium "white" liquors like vokda, gin and tequila, are a scam.
2) With wine, tannins are a known hangover cause and are highest in wines that are formulated to be aged. And wines that are heavily aged are usually on the higher end of the pricing spectrum which means that heavily aged, very expensive reds can cause worse hangover than cheaper wines.
3) To a lesser degree, the same can be said about dark liquors which tend to rise in price the more they're aged and the more time they spend in the barrel the better the chance to pick up impurities which supposedly intensify hangovers.
The real truth is that vodka and gin are better than dark liquors and dark liquors are better than dark wines. Ideally, the lowest hangover would be with really well filtered and well distilled vodka. But there's no way to tie that to the price tag of the vodka, more expensive most assuredly does NOT mean that it's purer, distilled better or made with higher quality ingredients. With some dark liquors and especially with red wines more expensive could be worse than medium priced. And they all cause hangovers. If you want to minimize the pain the next morning, watching price tags is not the way to do it. Drink less, eat a big fatty meal before drinking, alternate booze with water, etc.