Hello @erica_wagner ...
My guess is that your students are using the tools within the RCE (Rich Content Editor) to attach a file as a submission for the assignment...even though you are giving them specific instructions not to do that. I created a new assignment in my own sandbox course that was only a text entry submission. Then, I went to the Student View, and I was able to attach a file by using this tool in the RCE (See Screenshot 1).
Once the document was uploaded (or selected via "User Documents"), it displays like this in the RCE (See Screenshot 2).
After the student submits the assignment, the instructor can then go to the SpeedGrader, but what I saw in my own course was this (See Screenshot 3).
Rather than selecting the option for students to submit a file upload, the file just appears in the Document Viewer area as a link to the file...which you can download/view. For me, it did not display (unless I would select the option to preview in-line) in the Document Viewer. Further, if I chose to display in-line, the annotation tools do not appear because it's not technically a file upload...rather, it's a text submission where the student included a link to the file.
I hope this helps explain things a bit. Let us know if you have any other questions about this...thanks!