You seem to be suggesting that a connection is needed with
the DVD/VCR A/V inputs. But, if that's true: (1) Why doesn't
the above website mention it? and (2) How is the VCR managing
to record if the connections are wrong?

As long as the antenna or cable cable is connected to the VCR's RF input,
the VCR will record, regardless of whether the rest of the setup is
"correct".