I agree with Matthew's answer. Ohio is an at-will state, meaning the employer can terminate your boyfriend for no reason or any reason, as long as that reason is not discriminatory.
Yes, it's completely legal for the company to terminate him for the assault and battery of a coworker off company property. It's unfortunate and wrong that the coworker said what he did, but your boyfriend could have removed himself from the situation and discussed it with the appropriate personnel within the company rather than becoming violent.
I wish you both the best of luck.
Matthew J.P. Coffman
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Matthew and Rachel are right. In an employment at-will state, fighting with a co-worker, even outside of work hour and property, would be a legitimate basis for terminating your boyfriend's employment.
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