Yeah, my school did a better than average job. I think anybody attending a pricey private school deserves that much (obviously many of the osteopathic schools fall in that category). students' success is their success as far as it improves reputation & attracts better applicants etc. I don't understand throwing your grads to the wolves like this. Honestly it's even in their best interest to help ensure you get LORs and get them on time.
. . . and if you got instructions but chose not to read them, that's a hugely different situation than not being given any instructions.
I believe the absence of a chair is the reason it also says neurology clerkship director is acceptable. Beyond that you can also have a chair or clerkship director "designee"...who could be someone in a different department. I'll add my $.02, however, and say these letters are ridiculous, because the author often has not worked with the student. If I were the OP I would call his advising office to clarify whether there is a chair, clerkship director, or designee. If not, maybe they have a letter saying as much that goes with the MSPE. If not, I'd ask them to write one & I'd contact all the relevant programs, provide them with that documentation, and ask them what, if anything else, they want to further consider the application.
In the end, however, who here knows if this is even why the OP hasn't gotten interview invites -- it might just be typical for this process from the DO side.