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While Ohio is a right to work state, the employer can have a contractual clause regarding non-compete provisions and anti-solicitation provisions and those clauses are enforceable legally under Ohio law.
You have not provided the exact wording of the non-solicitation clause for us to review, but if it is a standard non-solicitation clause all it prohibits is you from actually arranging the new job for your co-worker or him arranging it for you and enticing the person to leave the current employer for the job. While your company might be threatening, if they cannot prove you actually enticed him to leave their employment for this job, they would not be successfully able to enforce that clause in this type of situation.
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