This stops more legitimate Florida claims than any legal defense does, and it deserves a straight answer rather than reassurance.
The money comes from a policy, not a person. In the overwhelming majority of dog bite claims the payer is the owner’s homeowners or renters insurance. They have been paying for that cover, often for years, for exactly this situation. Your friend is generally not writing a cheque and is frequently barely involved after the initial report.
Be honest about what it may cost them. A premium increase, a non-renewal, or an exclusion added for that dog. Those are real. Pretending there is no consequence is not fair to you or to them.
Now weigh the other side. If you do not claim, your medical bills do not evaporate. You pay them, or your health insurer does and then often comes after you anyway. Someone absorbs that cost. The only question is whether it is the injured person or the policy that exists to cover it.
Two things that help in practice: tell them early rather than letting a claim arrive as a surprise, and keep the conversation about the insurer rather than about them. Most people, told plainly, would rather their policy paid for your surgery than watch you pay for it.
And if the dog has a history, the claim creates the record that protects the next person.