That passage in the DoD COR Handbook was just to provide an example of how a government caused delay could be grounds for a potential claim by the contractor.  I personally agree with you that it's not the best example to use following the laundry list of items a COR should be aware of in order to not exceed their authority.

The passage also assumes the COR has knowledge of the work site and was supposed to verify it was ready for contractor activity.

In the real world, unless the COR was specifically tasked with making sure and coordinating that the work site was prepared for contract activity then the COR would bear minimal if any any responsibility.  But that wouldn't change the fact the contractor may have grounds for additional compensation due to a government caused delay.  Every scenario depends on all the facts.  In a case like this, a best practice would be to have a kickoff or post award conference to remind all the parties what their roles and responsibilities are.  Such a meeting might have reminded the contracting officer, the COR, and the contractor that the work site needed to be ready for contractor activity.   The standard for the government is that we must act reasonably, not perfectly.

By the way, the DoD COR Handbook re-write has been on hold for an extended period.  Unfortunately we have no idea when a new version will be published.