I think the reason is explained in the "tip"(provided in the lesson) which states that one always uses a stress pronoun after "plus/moins/autant de quelque chose que" (so moi, toi, lui/elle etc instead of je, tu, il, etc) and that the verb is never repeated (so one exludes the "have"/"had"/"do"/did"). Thus, the translation that "Il avait plus d'experience que moi" seems correct.
Agree with Susan - the point of the lesson is that, when comparing nouns, regardless of whether in English we say 'than me' or 'than I (did/have/had) etc', it is 'que moi . . . ' in French, and a French construct that uses a subject pronoun with the verb repeated is incorrect. There is no guessing involved as far as I can see, as there isn't a second correct answer to consider.
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