(back to the topic...)
Actually, not "above" but (apparently) in a diff thread. And you intentionally edited my quote and so misquoted me - I included an asterisk pointing to a list of exceptions, an important distinction.
However, that aside I tend to agree with you - technically there is nothing that says "must", and possibly, arguably the opposite. But the only concrete examples we do have are "Gifted" and very specific exceptions to "(clearly) Gifted".
Actually, nothing says that they must still be Gifted - there are stories of apprentices who "lost" their Gift in some terrible lab accident, and so were "failed" in that manner. Would they then be legit to help in a lab, simply because they bear that title, regardless of the presence of The Gift? It's perfectly unclear*.
(* By the rules, at least. In my mind, in many of your minds, the answer is less murky, and that's fine.)
Your logic is solid, yet borders on sophism - which is where linguistic logic and practical application so often part ways.
While, true, nothing in the Rules mandates "Gifted", nor is there anything that specifically invites "non-Gifted" despite some clear exceptions to "Gifted". While "logically" this means almost nothing (spec it means "neither Gifted is mandatory nor not-Gifted is necessarily invalid"), in practical terms of game rules it certainly does not give express permission to assume "other non-Gifted are valid". It does open the door to the possibility that "Other non-Gifted may be valid", that other exceptions may exist - but that would be on the shoulders of the SG to houserule in as they please.
And that makes perfect sense in the known context of AM rules, which time and again are, clearly and intentionally, loosely defined. Not "poorly" defined - the Authors don't want to tell you what must be unless they feel they absolutely have to, and take pains to phrase rules so they are both clear enough and yet not uninterpretably restrictive. So there is no "right" answer except for your saga, even if that doesn't fit perfectly with any consensus found here on these boards.
Go forth, be creative, have fun. It seems it would be hard to actually "break" this particular rules section, one way or the other (and even then, we won't tell).