Albeit if "AI-complete" is taken in a sense of generality and difficulty rather than "human-equivalent" then I agree much more strongly, but this is correspondingly harder to check using some neat IQ test or other "visible" approach that will command immediate, intuitive agreement.

This seems implied by X-complete. X-complete generally means "given a solution to an X-complete problem, we have a solution for X".

eg. NP complete: given a polynomial solution to any NP-complete problem, any problem in NP can be solved in polynomial time.

(Of course the technical nuance of the strength of the statement X-complete is such that I expect most people to imagine the wrong thing, like you say.)