There was a Mythbusters episode on this topic. With a blind taste test, an expert had no trouble telling the difference between cheap and expensive vodka... even after they did extra filtering on the cheap vodka.
It might depend on the nature of the cheap vodka. I once ran across a website that ranked various qualities of alcoholic beverages according to expert opinions.
With some types of alcohol, the highly-ranked stuff sold for hundreds of dollars per bottle. But Vodka had numerous highly-ranked offerings that cost only $20 per bottle.
I'm not doubting that Mythbusters show that you mention. Just because good vodka can be had cheaply, that doesn't mean that all cheap vodka is good. I expect that they compared bad vodka to good vodka, and am not surprised that experts could tell the difference.