I'm not sure you're actually disagreeing.
The OP gave a bunch of basic story concepts and expressed concern that they were too generic. But it's my opinion that story concepts don't really have any inherent merit or lack thereof. Hence my post.
What you're saying is that all the subsequent steps in the story development process are also made of ideas. But when we say "story idea," that's not really what we're referring to. What you're referring to would fall under execution imo.
I mean, what about writing *doesn't* fall under a broad interpretation of the word idea?
I'm just going to repeat myself Dragon. Although I will admit that many things are open to more layers of interpretation and "what this phrase means to me" than I can do justice for.
Now it's too easy to say, "Well the two sentences are just a starting point." No, this is the reflection of a philosophy that I believe holds people back. "I've got my idea, what's the next step? Right, characters..." You've now shifted mindsets, you've jumped to the next task, and now you're going to be stuck finding a compelling character because you've got your idea, when you should be looking at ways to continue to develop your idea chain with your character. The character, the plot, the setting - it's all part of that idea, still developing, still percolating.