It occurs to me that some OSR grognards regard any game where the players are given some sort of narrative control over the action as a "story game." To put it another way, some people think if you're not recognizing Rule Zero as a fundamental aspect of playing role-playing games then they don't consider it a role-playing game.
Rule Zero was always a stupid concept to begin with. The best D&D games I ever played in were ones where the GM built off of things the players handed them, and the worst D&D games I ever played in were the ones where the GM completely ignored the other players' desires and ambitions for his own plotline or slavish devotion to his setting. When I hear other people talk about their best and worst experiences at the table I hear the same kinds of stories, except when somebody is targeting a particular game. I try not to declare something is bad simply because I had a bad experience with it, or didn't have fun. I try to explain exactly what it was I didn't like without falling into generalized descriptions.
I don't like the Shadowrun system and I have only had bad experiences playing it, but that doesn't make it a bad game. I love a lot of things about Shadowrun despite my bad experiences and my distaste for the rules. I would definitely try playing it again with a fresh GM.
I don't like 4th edition D&D because it requires a map to play it, I think of it as a glorified board game, but that doesn't make it a bad game. When I get done playing a game of 4th edition D&D I am left thinking about the tactics I could have used rather than the story that was happening around, plot is incidental to the action on the table. It's just not a game that appeals to my sensibilities.
I don't like Paranoia because I have only ever had bad experiences with it, yet when people talk about what has happened in their games of Paranoia it always sounds like a lot fun. It's like when I hear about a sketch on Saturday Night Live and it sounds really funny when somebody describes it to me, but when I actually watch it it's not that funny. I could probably try playing it again if I was with the right group of players.
I don't like Monsterhearts because the playbooks are each individually defined to promote a very specific style of playing that particular character and I want to be able to have more freedom with my character then following a guided playstyle and narrative. I probably won't play it again.
I have probably had more bad experiences than good ones while playing 1st and 2nd edition D&D, but this always came down to a GM who either ignored what his players wanted to do or a GM who took possession of the campaign world in such a way that it limited the fun players at the table were having. The level-based system of D&D no longer appeals to me, but I would still play it as long as the GM didn't quote Rule Zero as a maxim for how they ran their game.