Assuming you had no employment contract stipulating the reasons you could be fired, then you were an employee at-will. Employees at-will can be fired for any reason or no reason, with the exception that the reason cannot be based on illegal discrimination (such as race, gender), or illegal retaliation (such as for filing a worker's comp claim).

Therefore, you could be lawfully fired for stealing even though you didn't steal. The courts do not reverse bad decisions, just illegal decisions.

PS: "Right to work" pertains to the right not to be forced to join a union upon being hired, and therefore, it has nothing to do with the question at hand.