This had more to do with the state and its rigid adherence to "At-Will-Employment" than anything else.
I am assuming that through this agency you are not under a union contract or any other kind of contract? Unless you are under contract, any employer in an AWE state (that's just about all of the 50) can terminate you with or without cause.
Now, if the institution soundly follows a process clearly described in say an employee manual, and they don't follow that process up to and through termination, then you may have some recourse.
See an employment attorney. It may or may not be worth your money, and as specialists, they tend to be expensive, and you have to make sure in using them there is no conflicts of interest with your former employer.
Generally AWE means you are screwed if they don't want you for ANY reason. So, if someone of influence doesn't like you or the way you part your hair, or b/c your teeth aren't white enough, or you are too smart, or cute/pretty, or somehow deemed a challenge to some folks of influence in the group--it's "See you later" time. Thus they may say, "It's not a good 'fit.'" Sometimes there is bogus stuff put in people's files. You may not ever get to see it, b/c, even with a lawyer, well, files can be multiple, moved around, you name it. I remember seeing two nurses changing documentation--that is right and the God's honest truth. Changing documentation to render someone "unfit" in their documentation and practice. If you think squirrely and illegal stuff doesn't happen in hospitals, think again. If weird stuff can happen through companies like Enron, yes, it can and does happen in hospitals too--yes, even those with all kinds of nice accreditation and other highly praised labels--like Magnet Status.
AWE seems like it's fair both ways, but really it isn't. This is why physicians and other professionals ONLY work under carefully written/worded contracts. Now, at the end of a contract, the employer may opt not to renew; but at least you have something reasonable and specific while you work there under contract.
Nurses need to start seeing themselves as professionals, and they need to start working under contract. There is just too much capricious nonsense within the hospitals with people today. No good nurse should be dismissed for capricious reasons--or under pretext or false causes.