Several people have suggested that limiting grant submissions is a 1rst amendment problem. Probably not. Remember the uni submits the proposal, and grants are made to the Uni. NIH does not permit submissions. This can be found in section III of a FOA. They tend to start like this:
Section III. Eligibility Information1. Eligible ApplicantsEligible Organizations
Higher Education Institutions
Public/State Controlled Institutions of Higher Education
Private Institutions of Higher Education
blah blah blah.
Finally at the end:
Eligible Individuals (Program Director/Principal Investigator)
Any individual(s) with the skills, knowledge, and resources necessary to carry out the proposed research as the Program Director(s)/Principal Investigator(s) (PD(s)/PI(s)) is invited to work with his/her organization to develop an application for support.