Hi Tim,
I think this is one of those moments when, as someone above said, failure to hit "Save changes" is the issue.
In Moodle 1.9, we found that students in this assignment who touched either "Notes" (if enabled) or the upload function , but didn't finally save were notified they had uploaded and the instructor was notified there was a submission.
Here's a workaround, but it is controversial. I give my instructors the "login as" capability. That allows them to login as a particular student, view the situation, and, if warranted, do things like close quizzes, complete assignment uploads, end lessons and so forth.
The potential for malfeasance, invasion of privacy, and so forth is obvious.
But, given my students are K-12, I'm willing to live with that. I'd suggest getting that capability/permission for your instructors. This would allow your instructors to close issues *as your students.* BUT, you need to make sure you're comfortable with this issue.
I.E., An uploaded file that hasn't been "save changes," etc.