In general, a student will ask to have their grade changed because they feel the work is stronger than recognized by their grade. (It is helpful to prepare a memo pointing out the strengths of the paper, in light of the above rubric.) In order to avoid moral hazard, as the economists call it, there is a possibility that a rereading of a paper will result in a lower grade. (Otherwise, if rereadings could result only in an unchanged or an improved grade, the incentive system would not encourage students to carefully think about the problems in their papers.)
On the other hand, students might feel that the professor could retaliate against them for even asking for a grade change. Hence it is crucial that there be oversight by the department or school. In the background is the fact that in a university, the professors are rationally presumed to have authority and integrity--although this is open to question. The professor can be challenged. But the professor's authoritative judgment is what the student is seeking. This is very different than most challenges to authority, because often those challenges are meant to negate authority.