I think the actual story itself is fake. Meaning, they didn't actually give anyone any vodka. They just made those bottles and filmed a few friends pretending to pour it at parties to use in their film clip.
I'd strongly prefer believing this too, but the part that mentions them receiving 'an email from Mercy Hangover Prevention' and then the picture showing their vodka + the 12-pack of Mercy makes me think the story is real, unless Mercy is owned by friends of theirs.