The data showed unambiguously that TAs who lost their accent were much better teachers than those who didn't. It wasn't about not being able to understand the words of the TA; there was an English qualification test that weeded out anyone who couldn't be understood clearly. I think the lack of accent was a proxy for other changes, like being adaptable and willing to alter one's behavior. The bad TAs with accents tended to use ineffective teaching techniques and not change while the good TAs updated their teaching methods based on feedback.
This fits well with my experience.