Background Check at First Interview? Should I go?

Sounds fishy, no? I don't know where else to put this, so I'll put it here since I'm in New Jersey. I just got off the phone with some recruiter for a social services staffing agency that places nurses in contract mental health positions. Mind you, I have been applying everywhere throughout Nj for two months with hardly a response. One of the staff members at a free clinic where I have been volunteering recommended that I contact this agency. She works in mental health at her real job, but does not know anyone personally at this staffing agency. But, she spoke to someone from this agency and they offered her a job. She said she wasn't looking because she already has the mental health gig, but thinking of me and trying to help, she asked them if they were looking for only experienced nurses. They said, not necessarily. So, she gave me their contact number. So, today, I called the agency and was thrilled that I got an interview. But, upon immediate reflection when I hung up the phone, this recruiter seemed a little too eager to get me in there. Within a minute of talking to her on the phone, she asked me to come in for an interview. She told me everything I'd need to bring, including resume, diploma, cpr card, drivers license and (and this is what really raised a red flag): a $27 dollar fee for a background check. First of all, isn't that a little inexpensive for a background check? Second of all, shouldn't they run the background check AFTER they decide to hire me? Is it normal practice for these contract staffing agencies to run a check at the first interview? Mind you, I have nothing in my background to hide from anyone. It's just that this seems to me like a great way to make a lot of money: interview a couple hundred people a week and collect 30 bucks a pop-- sounds like a great business. A search for this company on the New Jersey better business bureau website turns up nothing. Am I just being paranoid or am I just not that stupid? The thing is this: I'm in such a vulnerable position being unable to find gainful employment that I am ripe for being scammed. I am almost willing to entirely ignore this. Should I go to this interview? I can afford to lose 27 bucks, but not my identity (SSN), you know? I'd appreciate any advice. Thank you for reading.