Okay, I figured out the problem (lack of user knowledge) and decided to post the results so others may find the answer. Please correct me if I am wrong, but this is the way it seems to work.
To have download you must use some form of registration. The "no registration" option does not work, since they have no way to get to the order to see it. Hence, in the complete context of my question, I had "no registration turned on and the emails had no linked. With either "Simplified Registration" or "Registration" emails have the link. Now that I understand it, it makes perfect sense.