Sometimes the theft's all above board and fine. Like a folk belief I ran across recently, where mothers bake bird-shaped pastries, and the children spread them all about town, singing songs to lure the birds back, because they will bring the spring with them. The year it fails, the year the birds don't return and so the spring doesn't either. . . why it even has a built in quest!
You do have to settle for yourself, of course, who goes on the quest, and what is found at the end. Besides, of course, the birds. But you don't have worry about scrubbing off the serial numbers too hard.
Or the tale I ran across that ancient Chinese writers thought that only the Han Chinese were truly human. All other races were animals masquerading as human. Therianthropes only showed this fact clearly. (Whether it's true or not hardly matters. One of the delights of writing fiction, and fantasy at that.) Hmm, that may be connected to the way in Far Eastern tales, unlike European ones, a being that changes to a human being in the end might really have been an animal before, and usually was; in European ones, to end up human, you start out human. But, for a character to hear that tale and find out that it's false -- or that it's true, and the animal mock-men are just fine fellows -- or (he, he, he) that it's true, and the animal mock-men really are dangerous in some way -- the last would probably be a hard sell nowadays -- but, you notice, it doesn't include the character to find out all that or what sort of adventures he has in the process.
Sometimes, it is the characters. Imagine -- oh, imagine looking at the back story of Harry Potter and deciding invert the sisters. Rosa is the bright, beautiful one, sent off to wizard school; Violet, less pretty, quiet, sat-upon, and not sent to school. (Hmm. One would have to decide whether she lacks the gift or just isn't sent.) But Rosa's magical adventures lead to serious trouble, and Violet has to try to set them straight without magic. One could even have them grow up and marry, and then Rosa gets herself killed so that Violet has to take in her son and keep the magic from killing him too. But that one, to be sure, has only the characters, not the problem, or even the setting. (There is magic is not a setting. And, at that, one could situate in the far future with Rosa sent off to genetic engineer things. Though it would be harder there to fudge up a reason why Violet must fix it.)
Some ideas are harder to rip off. Like, say, the basic notion of Doctor Who. Still. . . .
A house. An Edifice, even, with rooms and hallways and stairs and doors that led outside throughout space and time. Inhabited by a genius loci, who not being human can change appearance, and often does. Plus anyone she has stay with her. Hmm. Whom she may call a housekeeper, which may, in fact, entail various duties to keep the house going. But in the meantime they can have adventures because she can leave the house. But it only has one character, and the adventures are kinda open-ended in possibility, and you can't have possible adventures in a story, you need real ones.
To be sure, you could probably get away with starting with a girl attending school, and two of her teachers being worried because she's so odd, and following her back to the house. This door looks like the building behind it is a junk shop, but when she goes in, she calls the genius loci Grandmother (perhaps the genius loci can take full human form, or perhaps the girl toddled into the house as the sole survivor of a massacre or something and the genius loci raised her). As grandmother, she revolts at having the teachers know and shunts them down corridors until they can no longer find their own door. She's a bit absent-minded and doesn't have all the destinations in mind all the time, and can't reliably get back to a door.
You could even call it tribute if you wanted to, if the details are changed enough. But even there there would have to be a lot of details -- and destinations -- that would have to be invented.