Proof that any key exchange protocol is vulnerable to MitM attacks in the absence of shared information or trust
It has nothing to do with information theoretic. You just need to construct an adversary and argue that it works. In this case, the adversary is simple. Let $A$ and $B$ be parties with no secret information. An adversary $C$ playing man-in-the-middle interacts with $A$ pretending to be $B$, and interacts with $B$ pretending to be $A$. At the end, $C$ establishes a separate channel with $A$ and with $B$. Then, any message sent by is decrypted by $C$ (using the key generated with $A$) and then re-encrypted (using the key generated with $B$) and sent to $B$. Likewise, in the other direction.

Since there is no initial secret, $A$ and $B$ see exactly the same thing as they would see in a key exchange that is not under attack. However, $C$ learns everything communicated.

The difference between this and a full proof is minimal.