Nonetheless, I bet some interviews leave them wondering if you can handle the work from an academic perspective. For example, if your spoken English is really poor (either as an English language learner or not) they will question your ability to contribute to the case method. Otherwise, I generally agree that the first check is to answer the "can you handle it" question.
I want to add that my guess is that for people on the bubble ("I wonder if they can handle the work?"), the adcom invites them to interview because the committee is willing to admit exceptional candidates with shaky quant skills. The question they are inadvertently asking is, "Are they worth it?" So by no means have you proven your complete academic chops in all cases. They are looking for a reason to admit you and hopefully the interview helps create that reason!