I don't have access to a computer running Word 2003 so unable to try that option. The document is a .docx file. I tried saving it as a .doc file but the same thing happens when opened in Word 2016 (the checkboxes aren't selected).

Attached are two screenshots - the first is the document in Word 2016 (the checkboxes are not selected), the second is the document in Word 2010 (the checkboxes are selected)

FYI - I've removed most of the content for privacy purposes but you can see the difference in the checkboxes being selected/not selected.