After playing around with it, I figured out something. Users CAN upload multiple attachments, they just have to do it in a certain order. One of the fields (Posting Message) is required, they have to type something in there, then TAB out (not click) and the Attach control is enabled. They attach one file, then have to do the same thing (type in posting message, tab out) in order to attach another file.
I tried making Posting Message not required. Doing that disabled the attachment control completely. These controls are not dependent on each other at all in the rules. I am lost.