Thanks for your question.
Let me first start by saying that as a lawyer, I'm confronted daily with people who do infuriatingly wrong things and I am constantly tempted to tell them that I'd like to "meet them outside." So, I understand where you are coming from.
The reason I don't do this, and the reason you should never say anything like this again, is because a threat of physical violence
qualifies as an assault under the law. An assault takes place if one person makes a verbal threat of violence to another person, and that person has a reasonable apprehension that the violence threatened will actually take place.
Now, you said "maybe we should settle this man to man on your lawn, outside of work" and this is actually a very vague statement. For all we know, you could be talking about a friendly game of horseshoes. There is no specific threat of violence here. If you had said "I'm going to kill you" or "if I see you I'm going to smash your face" or something similar, this might be a better example of an assault. So if a claim were actually made against you, you have an argument that there was no reasonable apprehension of physical harm because you did not make a specific threat of physical harm. Thus, no assault took place.
In regard to the actions they are taking by "warning" a third party about you, this could constitute tortious interference with an existing business arrangement and defamation of character. Your company should send a Cease and Desist letter to the the other company that warns against making any statements to any third party with which you are doing business that is negative about the company. You personally have a right to claim defamation of character against this fellow in that he has likely spread false information about you hurting your reputation to third parties (including his own HR department).
My advice is to tell your boss what I've told you and you should hire a lawyer to send an official Cease and Desist letter to the other company, suggesting that further communication should be avoided and that both businesses should walk away before the situation gets out of control and you are forced to go to court.
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