I used to get referrals from the San Antonio Bar Association. These referrals included many clients who had never spoken to a lawyer anywhere. Many of them would call complaining basically about unfair treatment. I still get calls like that, sometimes. They might say, "my employer fired me because they claim I did not call in, but I did call in." I have to explain to potential clients like this that in Texas, an employer can fire you for the wrong reason or even for a stupid reason. I have talked about this before.
We have what is known as "at-will" employment. An employer can fire you for any reason (other than various types of discrimination). Just as the employee can quit for any reason. So, yes, even when the employer is wrong, even when you did call in sick and the employer just flat messed up and did not record your call, they can still fire you. I wish that was not true. I wish our state laws were different, that they required some sort of "just cause" for termination. But, most states do not require just cause for a termination. Only some 10 states require a good reason for a termination. In the rest of the states, such as Texas, an employer can fire you for the wrong reason.