Teacher created an Advanced Uploading of Files assignment. Grade was set to No Grade
Students uploaded a file
Teacher downloaded file, made corrections, saved it as a different name and uploaded it as a response file
Teacher saved feedback (didn't give a grade since type was No Grade)
Students received notification that assignment grade was updated.
When students tried to access the response file it was not present although teacher could still see it in the grade window

After reproducing this, I set the assignment to receive a grade and then gave the student a grade.
The student could then see the response file along with the grade

Although there is an easy workaround, this does not act the way I expected. Teachers should be able to set this as a No Grade assignment and also give students a response file. The particular teacher who notified me of this problem did not want to use the Moodle gradebook, but actually gave the students the grade on the response file.