The lie is in calling it a labor shortage without qualification. There won't be a shortage of all labor, just a highly specific class of labor, and everyone else will be left out.
Instead of a signed legal contract, a DCO is an affirmation that a certain person confirms that it is (s)he who holds legal liability for the act of sending of the code, that makes it easier to shift liability to the sender of the code in the case of any legal litigation, which serves as a deterrent of sending any code that can cause legal issues.
This is how the Foundation protects itself, and the policy is that a contribution must have a human as the person who will accept the liability if the foundation comes under fire. The effectiveness of this policy (or not) doesn't depend on how the code was created.