Does "I Quit" Really Mean I Need FMLA Leave?

Imagine you have an employee who is out three weeks on a medical leave protected by the FMLA. The employee suffers from a serious mental condition (or some other chronic condition), which has required her to take FMLA protected leaves in the past. The employee is medically released to return to work without restrictions and returns to work. Then, on her first day back at work, she unexpectedly leaves work early. The next day she says she is not returning to work and submits a written resignation to that effect. However, three days later the employee wants to return to work claiming the resignation was a mistake, and she really needed additional FMLA leave. Do you have to reinstate the employee or face potential liability under the FMLA? In other words, can an employer rely on what the employee says ("I want to quit") or must it investigate whether the employee wants and/or is eligible for additional FMLA protected leave?