A perfect example of this question is the Help for the Cells
property. It says that in expression.Cells, the object specifier
"expression" is required, regardless of whether it refers to an
Application object, Range object, or Worksheet object. However, there
are plenty of examples where "Cells" is not prefixed with an object
specifier. In fact, the very Help page for Cells contains such an
example.

Where can one find clear rules specifying when the object specifier is
truly required, and what the implied object is when the object
specifier is not present?

May bad. I'm not reading the help slowly enough. It is described in
the Remarks. Sorry for jumping the gun.