Examples of files that have icons in Explorer but not Dopus include "Downloads," "Box Drive," Internet Explorer .exe files, and multiple others. I used ShellExView to disable cloud-type storage programs and I ran the ClearIconCache program, but no luck. I am using the current non-beta version of DOPUS.
It sounds like Preferences / Folders / Folder Display / Show generic icons for... is turned on for the type of drive you're looking at.
That was a very correct answer. Problem solved.