This is true. A game can be ruined by any aspect of it being handled sufficiently poorly. But, it depends more on how integral it is to the game as a whole than execution:
- A game with bad audio can be muted, unless sound cues are vital to the gameplay, or there are no subtitles for the story.
- A game with bad gameplay can have an easy mode that anyone can beat, but anything that has a realistic chance of failure is going to be a roadblock.
- A game with bad story is a problem if you need to pay attention to it to know what to do, or if choices in the setting result in poor visual designs.
- A game with bad visuals is usually hard to salvage. But, for instance, a game that has a party system, and there's a character with a horrible design, you can choose to not have them in your party.
- A game that is a sequel to something that doesn't have much to expand on is going to either be very limiting to what you can do, or will end up very different to its predecessor.
Generally speaking, the more important an aspect of the game is to the player, the more important it is to get that part right to appease them. But any part that integrates with other parts is going to have to be good, as well. A lot of games (that aren't things like visual novels) don't integrate their story to the gameplay at all beyond deciding what the game is going to be deigned to play like. In such games, cutscenes are the main way that a story can ruin the rest of the game. As long as the cutscenes are skippable, one can deal. Unless you want a good story in your games, in which case, nothing can save you.