Disney's lawyers are famously litigious. I'm not clear that they would win a case here. (Although they might have success with this HN comment as evidence)
The Adventures of Willy the Wizard: Livid Land (1987) has a similar high-level of comparison to Harry Potter and the Goblet of Fire (2000), and that case was thrown out.
"Both Willy [a wizard] and Harry are required to work out the exact nature of the main task of the contest which they both achieve in a bathroom assisted by clues from helpers, in order to discover how to rescue human hostages imprisoned by a community of half-human, half-animal fantasy creatures."
is very comparable to your completely hypothetical example above.
So, if a paragraph of cherry-picked, high-level description are the only identified similarities, there is no case in copyright law.