Yes, it seems like Gary included that awareness of the body, and you're definitely correct, sitting without an object is the essence of shikantaza.

My sense is most people need at least a minimal level of object awareness before they can really get to shamatha without an object.

The general Tibetan progression is:

awareness of breath

simple recognition of passing thoughts, emotions, etc

THEN awareness of awareness, or really, awareness without an object

And you're right, when that stabilizes, a very very profound level of insight, vipassana, is possible. "What is it that is aware?"