Thank you for your question.
The law in the US on employment issues is actually very lopsided in the employer's favor. It for the most part allows the employer to set up internal policies in whatever fashion the employer wants to. It also allows the employer to terminate an employee for any reason or no reason at all unless there is a specific employment contract
with the employee that provides otherwise.
In this situation, the company's internal policies regarding investigations and warning letters are not regulated by the law. So, whether or not you can appeal the finding in this letter is a matter completely up to the company's internal policies.
What I recommend that you do in this situation is send a formal dispute
letter to your supervisor and to the HR department and ask that it be included in your employment file. In the dispute letter you should explain as you have above, that you did not violate any company policy regarding contact with competitors and that the warning letter is not fair and is disputed.
If you have discovered a mistake of your manager regarding ISO standards, it might be wise to speak to someone in HR about this as well to determine whether the company has any reporting requirements that you need to meet.
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