Did a bit more research and going to share for anyone else who finds this thread. Apple uses FedEx for return (and repair) shipping and the most common risks seem to be:
(1) Drop package in FedEx Drop Box, package disappears / isn't scanned in
(2) Drop package at FedEx On Site (eg. walgreens), package is stolen by employee before FedEx handoff
(3) Drop package at FedEx Ship Center (actual FedEx location), package is stolen by employee
(4) Package begins FedEx shipment journey and is damaged / lost / stolen during transit
Then it's up to the customer to escalate with Apple until they get an acceptable resolution. Generally, it's possible to get a refund from Apple and Apple takes the issue up with FedEx. If you don't escalate the issue with Apple and get a resolution in a timely fashion though (<30 days) Apple can choose not to provide additional support (ie. not provide a refund / not follow-up with FedEx). It did seem like as long as you were timely in following up with Apple and comfortable escalating when necessary that Apple will (usually) provide you with a refund in cases when FedEx is at fault for return / repair shipment handling.
In the end I chose to return the phone in person to the Apple store. Personally I really didn't want to deal with additional unexpected stress if something did happen either immediately after handing off the package to FedEx or during shipment.