Can an employer go back on promising not to contest unemployment benefits?

I was informed by my former employer that my position’s salary would be cut in half & i could either (1) take the drastic pay cut or (2) sign a release of claims with a severance payout. my former employer made it a point to tell me in that initial conversation that should i accept the release of claims/severance payout, they would also NOT contest if I applied for unemployment benefits. Now I have to attend a hearing because they in fact DID contest my unemployment benefits and are saying I was essentially offered a job & voluntarily quit. Can they get away with this? I have an upcoming hearing. Why would they go out of their way to tell me they wouldn’t contest me filing for unemployment, just to turn around & do just that? Also: of course they would not provide me anything in writing other than the severance agreement. Other than my direct supervisor at the time & another manager in the room to witness the conversation, I have no written proof of the two options I was given.