By "verifying who controls the IP space", do you mean verifying control over the IP a domain resolves to? In that case, what you're missing here is that control

By "verifying who controls the IP space", do you mean verifying control over the IP a domain resolves to? In that case, what you're missing here is that control over DNS lets you alter that IP address to whatever you'd like. The attacker will have no difficulty demonstrating control over an IP address they own.