The request is not unreasonable, though privacy concerns may make it not possible, particularly for small classes. But this is a problem with the grading method, not the request. The student should be given some information about the grade distribution, or might reasonably request that an administrator or authorized party other than the professor confirm that the grade was calculated correctly and the grading is fair.
As a professor, I think that my students have an absolute right to understand how their grade is calculated. If I make that calculation depend on the distribution of grades in a class, then I've imposed a requirement on myself that my students have a right to understand that distribution, even if they don't know who earned what grades. If I want to obfuscate exact scores as an additional measure of privacy, I could show just a histogram, or announce the mean and standard deviation of grades.
If the student were not given this information, there are two very serious concerns:
- The student can spend the whole semester thinking they are performing adequately, only to find out that they were misled. To get a grade of D, the professor must think that student has exhibited a bare degree of competence, and is not ready to advance to higher level material. If the student was clueless earlier in the term because their numerical score indicated they were performing at a high C (what a 78 translates to in most American institutions), that student has not been served well by the course.
- Grading the student based on hidden information opens up the possibility that a professor could lower a student's grade for reasons not related to the student's performance (personal dislike, unconscious bias, etc.), and the student would have no way of verifying.
In courses I have taken as both an undergraduate and graduate student (in American institutions), when exams or courses were "curved" (i.e., graded in relation to the distribution), the professors would always give us some summary statistics (such as the mean score, or number of students in each letter grade bucket). As a professor, when I have curved an exam, I also would provide information on at least the mean, and maybe some other summary information as well. No one has ever indicated to me that this violates privacy requirements. But if, say, an administrator told me that I could no longer do that because of privacy concerns, then it seems that a faculty advisor, department chair, administrator, or someone else with appropriate authority to review private student records would have to be given access to all student grades in the course so that a student would have recourse if they suspect they have been graded unfairly (point 2 above).
I have to also say that in my experience when student grades are based on the distribution of other students' scores, it usually means that grades are raised relative to what they would have been using an absolute scale. I have not heard of someone using the distribution to lower final grades relative to what they would have been on an absolute scale. I never experienced it as a student (and would have been unhappy if it happened), I wouldn't do it as a professor, and I have not heard of colleagues doing it in their courses.
In summary, although it was not part of the original question, I think it has to be said that this grading system is pedagogically unsound because it seriously impedes the students' ability to understand their mastery of the material prior to the assignment of the final grade. Be that as it may, because the student has a right to understand how their grade is calculated, and in order to avoid the possibility of the professor assigning arbitrary or unfair grades, if this is the way a course is going to be graded, the professor has imposed upon themself the duty to publicize some information about the the distribution of scores in the course.