Thanks for taking the time to try to help me with this.
My primary source for this file is from Blackboard. I've tried downloading it several ways. The normal click-to-download causes Safari to not only add the .zip, but to unzip it and turn it into a folder that I can't do a thing with. If I control-click on the file link, I can "download as" and actually see that the file name is .docx [exhibit A that this is NOT really a zip file]... but by the time it shows up in the download window, Safari has changed that to .docx.zip (if I then look at it in Finder and change the file name to .docx then Pages opens the file just fine [exhibit B, Pages won't open a real zip file, will it?]).
I don't really think that Blackboard is the culprit, though (although it is a "usual suspect"), because I have also emailed the .docx file (that opens just fine on my computer) to myself and it arrives with .docx.zip if I send it using Safari (to access webmail.nku.edu - a MicroSoft Outlook Web Access way into my university email account)... if I send it through the same email link using FireFox, it arrives as a .docx that opens just fine.
My guess is that in the hidden bits of Safari there is a table of "known" file extensions, which hasn't been updated to include .docx (or perhaps some other part of the file type information hidden in the files). This would also fit with a discussion on the Safari threads, blaming Yahoo Mail for similar problems with Safari.