You should contact an employment attorney in your state to handle the appeal. Hopefully you have a copy of what you signed to show him/her. It's possible that the changes made could affect your situation depending on what the original and what the new versions say. It's also possible that whatever you originally signed may have barred unemployment benefits.
To answer your most important question first: Unemployment benefits are paid by the government, not directly by your ex-employer. So, whether or not you release each other does not matter if you otherwise qualify for unemployment benefits.
If the termination agreement is somehow fraudulent or altered after you signed it, you should point that out in the appeal, and be prepared to provide proof. If you have a copy of what you signed, that could be your proof. Or perhaps you can call as a witness your friend that still works at the company. When your friend is under oath for the appeal hearing, hopefully your friend will feel compelled to tell the truth even though it may jeopardize your friend's job.