I see this type of explanation frequently, and it’s misleading.

QKD does roughly what Diffie-Hellman does. One way to look at Diffie-Hellman is that two parties have a public but tamper-proof communication channel: Alice and Bob can talk to each other, everyone can hear them, but no one can impersonate them. (This could be literal shouting in a crowded room, cryptography could be used to authenticate messages, etc.) Using Diffie-Hellman, Alice and Bob exchange secret shares over the public channel, derive a secret key, and, assuming no one has a mathematical breakthrough or a quantum computer, no one else knows the key.

With QKD, Alice and Bob have the same public channel, but they also have a quantum communication channel, e.g. a fiber. This quantum channel is assumed to be completely insecure. Using both channels together and some math, Alice and Bob derive a secret key. For their trouble, they have a stronger sort of security compared to Diffie-Hellman — they don’t need to trust that their attacker doesn’t have some kind of breakthrough. There is an information theoretic proof that the scheme is secure as long as everyone plays by the rules. (Playing by the rules means no side channel or glitch attacks. A classical glitch might involve putting a very high voltage onto someone’s network cable to cause their NIC to malfunction. A quantum glitch attack might involve shining an extremely bright light into the fiber to cause someone’s hardware to misbehave.)

This is all that QKD does. It’s not magic, and the tamper-proof classical channel is required.