Assignment has recorded that a student viewed the assignment since at least 1.9. What it is really doing is saying "Student A has touched this assignment." I, too, find this confusing, if they don't submit anything. On the other hand, it's a nice way to track what students are doing.
Equally interesting, Student A can get all the way to uploading a file, not click Save Changes, and Moodle will say the student has upload 0 files.
This is true for Student A deleting a file that was uploaded earlier. Moodle will say student has uploaded 0 files.