Interesting, I think I myself was hung up on the word cocktail. I was going to say I've never had a beer cocktail, but half the huffpost list is variations on Shandy, so I reckon I've had at least that. I didn't really consider that a "cocktail". I know my wife like "red beer" but hasn't had it in a while.
To my knowledge, I've only had one cocktail with beer in it, but I'm really having to wrack my brain. I assume it was at a McMenamins since they tend to do wacky stuff like that, but I don't remember what it was, so it wasn't too memorable. I think it had whiskey and beer in it, but there was no way you'd ever know it had beer in it, the other flavors were too strong. I think the things on these lists are designed to make sure you recognize the beer in them, hence a beer cocktail, rather than a whiskey cocktail with a splash or float of beer.