You're right, I did misinterpret your question.
The Set As Default button should be enabled. The fact that it isn't may
point to some problem in the Normal.dotm template or elsewhere.
As a troubleshooting step, with Word closed, go to the Templates folder,
%appdata%\Microsoft\Templates
and rename Normal.dotm to something else, such as OldNormal.dotm. Then start
Word, which will build a new template from its internal defaults. Try again
to set the Word 2003 style set as the default. Is the button enabled now?
If it's still disabled, the cause could be an add-in. Try disabling them one
at a time (in Office button > Word Options > Add-Ins, select an add-in type
and click Go, and uncheck a box) to see whether that makes a difference.