A worker's comp carrier can try to subrogate against a third party if there's a possibility of liability/negligence other than the employer. For example, if you're a carpenter working for a construction company, but the ladder you're climbing breaks because of faulty materials or construction, your employer's worker's comp carrier will go after the general liability carrier for the ladder manufacurer. I suspect that's what's going on here...Some municipalities, particularly the larger ones, are self-insured for either worker's comp, liability or both, and may be leaving the officer hanging out to dry with her medical bills.
Having said all that, I think suing the family is an unmitigated act of the highest sleaziness.
If the WC isn't paying her bills then she needs to go after them with a lawyer, not the homeowner. Standing where the EMT's were administering CPR on a drowning victim and then slipping in the water should directly fall under WC, she needs to go after them, not the panicked family members who quite frankly at that moment would give a rats *ss if the police were there afterwords or not, much less a couple of cups of water on the floor.
I can't believe that she would go through with this knowing what the other officers she has to work with must feel about it deep down inside, with the publicity she is getting I bet she retires soon.
She dropped her suit.