This is a similar problem to "as well as him" or "as well as he".
In "She is older than he is", we consider "than" as a conjunction introducing a subordinate clause, of which "he" is the subject. If we remove "is", we can consider what remains in two ways: a) as an abbreviated form, with "is" understood, so that "he" remains the correct form. b) with "than" as a preposition f