It is my understanding that domain name forwarding is binary: if a domain name is forwarded to a valid site, it cannot simultaneously resolve to a valid IP address. Is this correct?
Domain forwarding is accomplished by pointing the hostname you want to forward to a server, then configuring the server to accept HTTP requests and forward any request to another URI.
This means that, in order for it to work, the DNS record for the hostname must actually point to an IP address, the address of the server that is handling the forwarding.
In other word, your statement is not correct. For the forwarding to work, the hostname must point (resolve) to a valid IP address.
"Forwarding" is typically used to describe a specific type of full site redirect. In that case every URL on the domain is 301 permanent redirected to the corresponding URL on another domain. For example:
To implement 301 redirects, the domain name MUST resolve to an IP address and there MUST be a server there that implements these redirects.
Many domain registrars and web hosting companies have dedicated servers set up for this purpose. They handle this forwarding for you on their servers. If you use the forwarding options from your registrar or host, then they will set the domain to point to their servers and do the redirecting for you.
There is nothing to prevent you from doing this forwarding yourself on your own server. In that case, it would be perfectly acceptable to have your DNS resolve to your server's static IP address. You would then have to configure your server to do the redirects.