Why is this not what you want? Are you using the reverse proxy as a load balancer to multiple servers? Otherwise, if it's 1:1 proxy (for something like SSL termination) wouldn't having nginx fail/timeout when the server does be acceptable?
That's extremely likely.
Somebody with an Nginx reverse proxy is probably using it for high availability, load balancing and static files cache, probably at the same time. This is what it is good for.
However what would really need to happen is to only disable proxy_next_upstream if data has been written or read from the backend(preferably configurable by backend or location for either of those two options). Right now you basically lose the redundancy in non-idempotent requests, and immediately return the error. Or maybe I read the configuration incorrectly.