I did it! MS Tech Support Was Wrong!
Even though MS tech support said I couldn't do it, I tried a "clean install" by booting my Win 7-64 Upgrade Disc and following standard procedures. (I had Vista 32 installed) The install doesn't ask for your CD key until much later in the install process. I was afraid that by the time I entered my CD key, my Vista would be gone.
My upgrade CD key was accepted without a problem. I was not asked to insert the Vista disk. It just worked! I have succesfully activated the Win 7-64 installation with MS so I am sure I'm good to go.
So it is possible to clean install from Vista 32 to Win 7 64!!!