You're arguing two different points here. "A VPN can act as a proxy" and "A VPN that only acts as a proxy is no longer a VPN". I agree with the former and disagree with the latter.

A "real" host-to-network VPN could be used as a proxy by just setting your default route through it, just like a simple host-to-host VPN could be NOT a proxy by only allowing internal IPs over the link. Would the latter example stop being a VPN if you add a default route going from one host to the other?