There are several attack methods that apply even if both endpoints are on a "locked-down, secured" network segment:
DNS hijacking. Attackers may be able to poison or spoof DNS records for the server, thus causing the client to connect not to the legitimate server but to an illegitimate server.
BGP hijacking. Attackers may be able to attack BGP to cause packets to be routed, not to the legitimate server, but rather to the attacker.
Eavesdropping. Attackers may be able to eavesdrop on the data as it traverses the path from the client to the server. Even if the client and server are each individually on a network segment that does not allow eavesdropping, the attacker may still be able to eavesdrop on some intermediate hop halfway in between the two endpoints.
In each of these attack scenarios, all security is lost if you are not using any form of end-to-end crypto. Securing the network at the two endpoints does not stop any of these attacks.
P.S. There ain't no such thing as a secure network. I don't care how much "locking down" you do. When you throw around phrases like "locked down, secure network", it makes me think of marketing hype: e.g., maybe you've been fed some marketing documents and are repeating them. If so, beware that reality doesn't match the nice-sounding phrase.
(Other phrases that should raise red flags for you include "unbreakable", "military-grade cryptography"/"military-grade security", "patent-pending encryption algorithms".)