So what you're saying is that instead of running their own Status Page on their own infrastructure that's reachable. They should outsource it to statuspage.io and pay another company to do it?
Yes, that's pretty standard. Availability monitoring and status reporting should be external and separate from your own infrastructure, otherwise neither may be available when you need it the most.
They do have geo-region (not just AZ) redundancy and failover, which puts them quite a bit above most home-grown company status pages in my experience. But yes, if the problem was for example in R53 it would indeed be better to have an solution without that AWS dependency.
Eh, as I remember it they have stuff in multiple AWS regions. Would take a global AWS failure to bring them down. This was my justification for going with them while working somewhere that used AWS.
That said, while it is extremely unlikely it shouldn't be discounted as impossible.