If it's an obscure result, it's reasonable for them to expect a student to prove it, I think. I mean, if not then basically every result with any sort of use would be given a name and markers would be wasting all of eternity looking up obscure results because someone thought "hey, that's just an application of #NAME#'s theorem".
It's like turtle's "well-known fact" result, it's just not practical.
Likewise, the arguement about the third derivative - it's certainly valid, but has the student learned how to use it or are they just taking something told to them on faith?
Whilst in practice a lot of the syllabus could just be taking things on faith, there is meant to be at least a veneer of encouraging understanding in there.
{Calling the third derivative result 'obscure' might be being a bit unfair, but it's not something the marker can be confident the student knows the reasoning behind. At least with the others, if the student uses it the marker can be fairly sure their teacher's tried to explain it to them}