How to provide information about past students without violating FERPA
Intuitively I would think that if signed consents were needed, NIH would instruct you to include them in your application or, at least, to obtain them and keep them on file.
I checked a few universities and found that they publish an email address for addressing FERPA questions.  Also, there is a contact page for the compliance section of the Department of Education: http://familypolicy.ed.gov/content/family-policy-compliance-office-contact-information
On p. 9 of the instructions you linked to, there is a contact page.
I'm not sure if it's relevant, but on that same page, I read:

Collection of Personal Demographic Data
NIH collects personal data through the eRA Commons Personal Profile. The data is confidential, and
is maintained under the Privacy Act record system.
http://grants.nih.gov/grants/collection-of-personal-demographic-data.htm

The part of FERPA that looks like it might be relevant is here.
The basic idea that I got about this is that NIH commits to holding the personal information you share with it as close to its chest as your university does.  In other words, it commits to using the personal information you give it for internal purposes only.  My big-picture view of FERPA is that it provides protections to students from having their personal information publicly disseminated (subject to a ton of fine print).