Although we have done a lot of experimentation, right now this is how things stand:

Our Downloads are NOT Virtual Products ...

Our Downloads are NOT Always Free Shipping ...

We have already put weight on the "DVD" Attribute itself ...

Yet the shipping method window still appears:
"Shipping Method:
This is currently the only shipping method available to use on this order."

freeshipper

BTW Zen Cart 1.3.7 because of some customization to templates I doubt we will be upgrading.