Professor will not write a letter of recommendation because I have restricted access to my records under FERPA, is this legitimate?
David Z's comment is dead on: it is an unpleasant technicality that under FERPA regulations, one should not discuss the student's performance in any quantitatively specific way. E.g., one should not say "Mr. X got an A in all my courses" or even "Mr. X was the top student in the course". The exact rules are confusing to many faculty members, to the point where one feels like if one took FERPA too seriously one might not be able to write a suitable letter.
In my university there is, in theory, a form that a student can fill out to waive the FERPA regulations on a letter-by-letter basis. In theory this means that if the letter is getting mailed to N institutions, one should fill out N forms.
(The above considerations apply to all students, not just those who have asked for special protection. However, a student who places further restrictions on their records is precisely going on the record as being especially concerned about their privacy, so in practice it makes a lot of sense to take the FERPA restrictions much more seriously for these students.)
It may or may not be the case that Dr. Z is himself trying to access or view any of your academic records. (I guess he must have done something to find out that your records are FERPA-restricted though.) Whether someone would look up a student's grades in courses taken by other faculty members must depend on the people and the institution. For instance, at my institution I have access to the grades of all undergraduate students -- and I have been informed of the FERPA requirement that I access them only for legitimate, educational purposes -- but I do not have access to the grades of any graduate students, even my own advisees. So in practice when I write letters for students I speak only about their performance in my courses -- but again, if they were FERPA-restricted and I was being suitably conscientious then I would even then have to be extremely careful about what I could say and likely be forbidden from including a certain amount of positive information about the student.
Also:
I have no reason not to remove the FERPA restrictions, but I hate the thought of removing them under these circumstances; this tastes a little too much like blackmail to me.
Even assuming that Dr. Z wants permission to access your records and not just to talk about them, I think you are not viewing this in the right way. "Blackmail" seems ridiculous to me: one of the conditions for that is that the blackmailer must have something to gain! What does Dr. Z gain if you waive or even entirely remove your FERPA restrictions? The pleasure of viewing some of your academic records??
For my part, I am curious as to why you chose to place restrictions on your academic records at all: what are you protecting yourself from, really? It sounds like you may not completely understand what FERPA restrictions mean and may have just taken them on as a sort of free insurance. If I were you I would learn more about this. In my opinion, one could argue that "I have FERPA restricted my records" and "Please write me a strong recommendation letter" is already a bit of a mixed message.
By "FERPA restrictions" I assume you mean additional restrictions on the release of directory information, since these are the only extra restrictions I'm aware of. If so, then the professor's reluctance may have little to do with your academic track record per se.
Many professors take a fairly laid back approach to FERPA and consider that an e-mail request for a recommendation constitutes sufficient written permission to release information. However, some universities take restrictions on releasing directory information very seriously indeed. As I understand it (keep in mind that I am not a lawyer), when you invoke these restrictions the university is not even allowed to confirm to anyone that you have ever been a student there. A few students deeply care about this, such as celebrities, the ultra wealthy, or anyone trying to avoid a stalker or abuser. These students have good reason to worry about invasions of privacy, and they want universities to place absolute restrictions on even apparently innocuous information. For example, you can imagine social engineering attacks in which a private investigator, tabloid reporter, or stalker forges an e-mail to a professor asking them to serve as a reference for a job or internship, and then calls them to dig for information.
For most other students, FERPA restrictions can be problematic. For example, if a company contacts the university to try to verify your resume, the university isn't allowed to drop any hints. They are supposed to give exactly the same response as if you had never been there, so your resume should fail to verify, and the company may not give you a chance to explain. (You'd think they should, and they might if they really want to hire you, but big companies can be pretty callous about quickly dumping applicants whose resumes fail to check out.)
In my experience, universities differ in how vigorously they enforce these rules. For example, lawyers are more influential in some administrations than others, and some universities simply have more celebrities enrolled and thus face greater pressure to be strict.
As for how the professor could find out you have these restrictions in place, I'd guess it was from looking at your records. However, there are other possibilities. Some universities specifically notify everyone whose class contains a student with extra FERPA restrictions, to remind them not to reveal that this student is in their class, so the professor might remember receiving these warnings.
So my interpretation is that your university has you on a short list of students for whom everything is supposed to be completely confidential, and this professor doesn't want to risk upsetting the administration by violating these restrictions (while your other letter writers may not have been paying attention or may be more relaxed about such things).
Here is what I tell my own students; my guess is that Dr. Z. is thinking along much the same lines:
"Federal law requires that I have a FERPA (Family Educational Rights and Privacy Act) release from you before I tell anyone other than a school to which you have applied anything about your education at this institution. For most of you, all I know about you is your performance as a student, so without that release, the most I can say is that you were my student, period. Because those asking about you are likely to interpret such a stark statement negatively, I won't provide any reference at all (except to other schools) without that FERPA release."