That Florida law only applies to HMOs and not PPOs. And just reading everything Dave has posted over the years points to him having a PPO and not a HMO. Either that or he over stayed in an out of network facility, which is all to common for people receiving emergency treatment in an out of network facility.
Heres a nice little link about balance billing. Notice the vast number of no's in the out of network columns.
http://www.statehealthfacts.org/comparereport.jsp?rep=66&cat=7&rgnhl=11#notes-1
So to sum up
Balance billing in expressly prohibited by in network providers, that even applies to out of network providers in a in-network facility in most states.
Completely out of network(out of network facility and provider) balance billing for emergency services is illegal in 9 states. Some insurance policies will cover balance bills. Some don't. Historically a lot haven't.
Dave's situation is not RARE, unfortunately it is all to common. That is why there have been roughly two decades of debate on the issue. That is why 9 states have banned or severely restricted the practice. Half of them since ACA.
And again, this is it is a good idea for people to have have separate medical emergency/medical evac plans.
Its also a good a idea for people to understand that their policy doesn't cover care after the emergency is over and they are stable but still in the hospital. Unfortunately most don't understand that.
But again balance billing is still alive and well for A LOT of out of network emergency care and will be unless it gets banned under federal law but that is highly unlikely.