Yes, forget all these issues about what the employer can or can't or is supposed to do. They can pretty much do anything they darn well please. Your going back into the room and begging them to help you and asking was I fired or not yada yada yada did not do you any good as far as making them want to terminate or not terminate you.
But if you have believed them or somebody else who said you can't get unemployment insurance, forget that, and file yourself a claim for benefits. Stick with the reason you were told when you were terminated as to why you were being terminated. (Regardless as to whether it was by phone, word or letter) Do not bring in everything else in the world like they were mad about this and that and they weren't paying the employees this and that. That's not relevant to your situation.
But yes, even if you are terminated, you can get approved for unemployment insurance if the employer cannot show they had a good work related reason why they terminated you. And as swalsh says, there's a pretty good chance that what you say is the reason they termed you is not going to disqualify you for benefits. The employer does not get to say whether or not they want to give you benefits, they don't decide that. And you have absolutely nothing to lose by filing the claim.
It is also the ONLY recourse you have, as there is no bureau of fairness or court case or anything that you have to appeal, fight, sue about, etc. in this at will state.