You are correct.

However, that specification is not trivial. Almost nobody correctly articulates property 1 when first encountering the problem if they do not already know the answer or are already aware it is a trick question (and even then most software developers still fail).

Furthermore, that also sidesteps the problem of formally specifying what a permutation is. Unless you have a grab bag of already proven powerful theorems, the author is most likely also going to make a error doing that as well even if we start at a proof abstraction level comparable to normal programming.

Reality is that trivial problems admit trivially wrong specifications exceedingly easily. There is little reason to assume that much more complicated problems that are hard to even articulate will magically support obviously correct specifications that are simpler and more understandable than the code.