If they are not for profit, they should qualify, (see update below) but the thing is, I can't find anyone who has actually gotten approved for PLSF even tho some people have been eligible for over six months now. The latest thing I saw, said that the loan servicer's couldn't verify that you were eligible. But if they can't do it, who can?
Right now you take the form to HR, and have them send it back to your loan provider. I think it may eventually be forgiven, but I would bet dollars to donuts you will end up going more than 10 years waiting for 'approval' on the actual forgiveness part.
Edit: I have found one person, thanks finance forum:
An Interview with a Person Who Received PSLF Forgiveness - The Biglaw Investor
Little light on details, like the ways it can be weaseled out of, but we have success, so thats good.
Heres some more on weaseling:
https://studentloanhero.com/featured/pslf-loan-forgiveness-approval-letters/
Edit 2: IMPORTANT: This is scary as heck "The ABA suit aimed to hold the Dept. of Education to the initial employer certifications sent through FedLoan. But in its response, the Dept. of Education seems to make it clear that such certifications are not official approvals for PSLF. The FedLoan letters do not guarantee in advance that payments qualify for forgiveness.
Instead, the borrower must make 120 qualifying payments and then submit an application for Public Service Loan Forgiveness. Only after an official application is in will the Dept. of Education make an official approval or denial.
You must make PSLF payments without knowing if you qualify"
So get the letter, but it looks like it doesn't matter, if the government wants to reject it, they will.