There is a way that a student can access their instructor's 'grade' view and modify grades, or modify an assignment. It is an obscure way, but nevertheless possible.
What I did is to right-click on an assignment and chose 'send link'. This gave me the entire URL of the assignment. This is an example:
I logged in as the instructor of that same site and opened up the URL for the 'grade' link of that same assignment. This is the link I got:
If you are a student in the class and type in the last URL, then you get the same access as the instructor's grade option. You can change grades and such.
There isn't a lot of differences between the two links above:
change doView_submission to doGrade_assignment and Reference to Id
Student might learn of the structure of the links by creating a site themselves, viewing the links and trying it themselves.