I feel like being pedantic for a moment. Our suburban posties don't get off the bike to deliver the letters, they ride up alongside the letterbox and deliver the letters right from the vehicle, as can be seen in the link in the GGP comment. They also deliver small parcels that will fit in a standard letterbox.
You are quite right though, as soon as the rain starts, they're in full wet gear. Bright yellow, you can't miss them.
Suburban parcel delivery is specifically taken care of by Startrack, an Auspost subsidiary, usually in a trusty Toyota Hiace van.
Additional protection would keep them 99% dry instead of 90% dry even in a storm. Right up to the point where they have to deliver a letter, where they would be 0% dry.
It's more important to be able to get in and out easily.
"Protection" does not mean absolutely proof against. But even more, "calling BS" implies that the statement is not just wrong, but deceptive, and I completely disagree with that premise. (Which is additionally a claim it would be idiotic for them to make for an occupant likely wearing a rain coat.)
Calling BS on this. Anything more than a light drizzle (or any kind of wind + rain combo) and that driver is getting wet.