Hello again, Ken.
Since you are a union employee, the bargaining agreement will typically set out the procedure for challenging any action by an employer, which normally includes filing a grievance about any action taken against an employee.
You indicate that you do not trust the union representatives and if you do not expect them to represent you fairly in any grievance, then it would typically be best to retain your own private attorney to assist you in this matter.
Since you indicate the statements placed in your file are false, you would typically draft a letter to the employer disputing the facts set out in the statement and setting out the facts as you know them with regard to the "incident" you refer to, but it is typically within an employer's discretion what to place in an employee's file.
Unless they are threatened with litigation through an attorney representing you, it is unlikely the employer will remove the document in question from your file normally.
I hope this helps clarify the situation for you. My goal is to provide you with excellent service – if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate my service when I have answered your questions so I will be compensated for my time assisting you. Thank you!