If you check out the linked study, it doesn't do such debunking. It found no association between hangover severity and vasopressin and it wasn't clear what other markers of dehydration it measured. Note that measuring dehydration accurately could be difficult and different people might experience different levels of dehydration differently. It should be the default assumption that there are many mechanisms involved in hangover, because the effects of ethanol are very complex.

One reason for the myth about dehydration would be due to "drinking plenty of water" still being one of the most effective things to do: If it's about the liver breaking down alcohol into toxic Acetaldehyde, drinking lots of water to flush it out. Understandable mistake to go from "more water fixes the problem" to "problem must've been not enough water (dehydration.)" This was how it was discussed in my university chemistry class. Also mentioned: a similar breakdown (same enzymes or whatnot) happens with methanol, and the breakdown products (formaldehyde and then methanoic acid) are stronger / more toxic than those of ethanol (acetaldehyde / acetic acid.)