Did more investigating. Turns out, I believe there is a bug at work here.
Scenario: cloned shape on same page.
>> if the clone references the reference shape directly, i.e., using field insert formulas such as SHAPETEXT(reference!TheText) or SHAPETEXT(Sheet.1!TheText) => both work using duplicating <cntl>+D, or <cntl>+left mouse. But copy/paste <cntl>+C / <cntl>+V FAIL This is the bug!!!
>> if the clone references the page shapesheet, as Nikolay indicates, then all is well.
Scenario: cloned shape on a different page than reference shape
>> the above formulas fail because there is no off-page reference. The formula must be Pages[Page-1]!SHAPETEXT(Sheet.1!TheText) in the case of direct shape referencing. Or, must be appended to the beginning of the forumula presented in the Nikolay case. For either of these, the editing must be performed on an off-page. It cannot be done on the page containing the reference.
There are two things to note:
a) this shape may be copied to page-1 and still work. The copied shape may be re-copied to other pages and still work.
b) with off-page formulas, Visio does not like using named shapes. So "reference!" will not work.
See attached. The light gray shapes were copy/paste of dark gray. Both have direct shape references and fail. The Yellow is the Nikolay case, but no off-page capability. The magenta is direct shape reference but includes off-page reference. Creating of the magenta shape must be performed on an off-page. Then, that shape may be copied/re-copied anywhere.