That he is complaining about his email being down or that he trusted AWS at all with email?
(to clarify: DNS+domain at the same service can be OK, as long as you have nothing else there. As soon as you start having other stuff, keep the DNS there, but move the domain registration away. Depending on which domain make sure you have auth keys, access to the admin domain or whatever would enable moving the domain without registrar cooperation. In my hosting days I did my fair share of emergency transfers and infrastructure to help companies get their basics online again after a SNAFU - totally doable to have first mail coming in again within a working day)
Yeah, no that's not how it works with email. You have to build reputation for weeks or receivers throttle you.
For outgoing emails, reputation is a huge issue, but at the same time it’s also fairly trivial to set up a (different) 3rd-party (gmail, outlook, sendgrid, whatever) with previous reputation so you can get back communicating.