Employee filed a work-related lawsuit against a company owned by ours–what are our retaliation worries?

Q: “A subsidiary company of ours wrongfully fired an employee while he was on workers’ comp and FMLA leave. He filed suit, then came to our parent company and showed that he is very knowledgeable and asked to be promoted. A supervisor then found out about the lawsuit against the subsidiary. Our supervisor refused to promote him five times. He also told the employee directly that he can’t expect to be promoted when he is suing the subsidiary, because we are the same company. The supervisor then transferred him out of town, and now the employee is complaining of retaliation. Are we in trouble?” – Dave, Nevada