Don't worry, Faust, you're near enough the right of it. You are just looking at the matter more abstractly than the dictionary is.
A premise is just that which was said before. However, we've come to usually take it as being specifically "that which was said first." What was probably the first important thing that was said during the development of Snapes on a Plane? "What if Severus Snape got on a plane and caused havoc with magic?" That's your high concept, and that is also the starting point.
Look at a standard 5 paragraph essay. The last paragraph should be the conclusion. The premise of paragraph 5, then, is paragraph 1-4 (since, in comparison, those paragraphs all came first). But that is different than the premise of the essay itself (which is in paragraph 1, the thesis statement [more or less]).
Tush, it might be useful to think of the original Latin. "Premise" is derived from the word "mittere." The word "missive" is derived from the same. A missive is a letter, a recording of your thoughts. A "pre-missive" is a letter before that, recording what you thought before.
Thus a "mise" is what you are saying now, with a "premise" being what you said before. Does that help?