Diffie-Hellman is what you use if you trust that the public key belongs to who you think it does. In many cases, that's totally fine. It'll either be hosted on

Diffie-Hellman is what you use if you trust that the public key belongs to who you think it does. In many cases, that's totally fine. It'll either be hosted on their server, or even hard coded into the client application you're communicating from. RSA + DH is the attempt to deal with an untrusted public key.