I agree with you!!! What is even more strange some of these institutions have their curriculum online and even share with students in their 'student handbooks' a very detailed syllabus. So I dont understand why the 'big secret' when it comes to sending to the NNAS.
In some instances though, the NNAS does verify with the school, although the applicant is never made aware. I know this because I happen to work at a nursing institution. They send what they refer to as an RFA (Request for Assistance). Its basically a form which has to be completed by the authorized person who completed the documents for NNAS. After verifying the authentication of the documents, this authorized person is required to sign several times then stamp in a place provided. The document is then scanned and sent back to the NNAS via email. Part of the reason for this form is not only for authentication purposes, but to ensure that the signature of the person who completed the forms are legit. The interesting thing though, the NNAS does not indicate that they are verifying documents for which applicant- but it can easily be figured out once you know who have submitted from the institution.
Also, when my file was on hold for a while I called to inquire of my status and the agent divulged that they were awaiting an RFA from my school. When I contacted the institution, the secretary confirmed that they had received it (although no connection to me was indicated on the form but because I was the only applicant at the time and also because the RFA was sent to the schools office email we knew it was for me). My account was updated 24 hrs after this document was submitted by the school.