However, the HTTP_HOST header is not optional (in HTTP 1.1) and most web servers require it to be right anyway to select the right virtual host.
Any gateway or proxy which strips the "Host:" header will stop 90% of web sites from working, so I don't think that's very likely.
So it's not a major dependency.
Moreover, the server may not have set SERVER_NAME to the same name that the client used.
So I argue that using HTTP_HOST is more likely to get the answer the OP wants.
Mark