What would you do? When FMLA turns into tropical holiday

Periodically, we ask three managers how they’d handle a difficult situation at work. Today’s problem: A top performer appears to have “gamed” the company’s FMLA leave system.
The Scenario
Manager Irene Palmerson marched into HR manager Christopher Simeoni’s office. “I need to talk to you about Kirsten Gates.”
Chris looked up from his computer, surprised. “Really?” he asked. “I think that’s the first time I’ve heard those words  in the 20-plus years Kirsten’s been working here.”
“I know,” said Irene. “She’s one of my best staffers. But she’s really done it this time.”
“How?” asked Chris. “Isn’t she out on FMLA leave taking care of her mother?”
“That’s just it,” said Irene. “That’s what she’s supposed to be doing.”
Caribbean caregiving?
“Supposed to be doing?” asked Chris. “Better sit down and tell me what’s going on.”
“Well, as you know, Kirsten’s mother has been pretty sick,” said Irene. “Over the past couple of months, Kirsten’s taken lots of vacation time to take care of her.
“Last month, her vacation time ran out, and she put in for FMLA leave,” Irene continued. “But now, I’ve just found out she’s spent the last week of her leave — her supposed FMLA leave — on vacation in the Caribbean.”
“You’re kidding,” said Chris. “That doesn’t sound like something Kirsten would do.”
“No, it doesn’t,” said Irene, “but it’s true. If it was anyone else, I’d say we send her packing. But you know she’s so good at what she does that she’d get snatched up by one of our competitors in a heartbeat.
“So what do you think we should do?” asked Irene.
If you were Chris, what would you say or do next?
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What your peers had to say
An HR director in Washington, DC

What she’d do: I’d try to determine if Kirsten was actually on vacation by getting in touch with the doctor who signed off on her FMLA leave. I’d gather info on what type of care Kirsten’s mother needs, where the parent is staying or recuperating, etc. If in my research I find that Kirsten had been in the Caribbean, I’d fire her on the spot.
Reason: Kirsten is abusing a benefit, and that’s simply not acceptable. Not only are we holding her job for her while she’s out on “leave,” but someone else has had to pick up her workload. If she’s not being honest here, how can we trust her going forward – even if she is a quality employee?
An  HR manager in Louisiana
What she’d do: When Kirsten returned to work, I’d call her into my office and ask her about her leave. If I discovered that she’d been in the Caribbean, I’d consider letting her borrow vacation against future vacation time earnings or I’d classify the time she was in the Caribbean as leave without pay.
Reason: If Kirsten is a quality, long-term employee, we want to maintain that relationship. At the same time, in fairness to the other employees, we can’t just look the other way. This is a fair compromise.
A CFO in Ohio
What he’d do: I’d conduct an investigation by getting more info from Irene, speaking with Kirsten, etc. If she lied to us about taking leave, I’d fire her.
Reason: We always give employees the benefit of the doubt, which is why an investigation is necessary.