Is it legally dangerous to terminate this worker given his health issues?

Q: We have an employee who has been going thru some difficult personal issues related to his health and overall well-being. I believe he is going through similar issues at home with one of his children. He recently passed out at work and was taken to the hospital by ambulance but was given the “all clear” by his own physician and the physician we sent him to separately. Even though I have warned the company of this employee's rights under FMLA, they do not believe that whatever is going on with this employee will be resolved within 12 weeks and they wish to terminate him, against my advice. Would this be leaving us in danger of a lawsuit for not allowing the FMLA time first? – Anonymous, Illinois