In an at-will state no cause for termination is required. Subject to the exceptions I mentioned above, you can be fired just because the boss doesn't like you. So even if an employer lied to you about the cause, that would not give you a case. And even if it did, subordination or not is subjective. Your interpretation of subordination and the employer's are likely two different things. Unless you have a contract or can point to an employee handbook that gives you certain due process rights in connection with a termination or can show that as a matter of practice the employer has given others due process before a termination, you are SOL.
https://www.usa.gov/labor-laws#item-35277
Wrongful Discharge/Termination of Employment
If you feel that you have been wrongfully fired from a job or let go from an employment situation, you may wish to learn more about your state’s wrongful discharge laws.
Wrongful termination or wrongful discharge laws vary from state to state.
Some states are “employment-at-will” states, which means that if there is no employment contract (or collective bargaining agreement), an employer can let an employee go for any reason, or no reason, with or without notice, as long as the discharge does not violate a law.
If you feel you have been wrongfully discharged or terminated from employment, you may:
Contact your State Labor Office for more information on wrongful termination laws in your state
Seek legal counsel if your employer terminated you for any reason not covered under state or federal law.
You may also be eligible for unemployment compensation and extension of your health care benefits.