Stop with the "they should have landed here or there". If you have ever gone down at low altitude with no power you simply look ahead and pick the best thing in about 3 seconds. Interstate would be high on the list anyway.
As for the why, likely fuel exhaustion or birds. Simply not enough fire spread with a wing ripped off spilling 30 mins reserve fuel all over the place as the airplane spun around. It ignited on impact probably due to massive compression like a diesel engine. Charter ops usually have a decent fuel contract at the home base and try to buy as little as possible while out. This 2 leg trip would have been possible without a stop, but no room for error. They would have known as the EICAS would have told them. As far as frozen fuel no way. It would have been good and warm from the oil heat exchangers. Could have been an issue with fuel quantity sensors. And they had less then they thought, but still both engines failing at same time has me perplexed. Even with exhaustion its unlikely for them to fail at the same time.
Birds? Naples has pelicans, trust me small birds do little to these engines. I have hit a ton with no issues. But its plausible.
Single engine failure and shut down the good engine? Possible.
You cannot restart those engines without apu running. On a charter I would expect them to start it on landing to save hours and fuel. As for the rat, it will deploy when no power to main bus if I remember correctly. I had to deploy one for testing and as soon as you turn off power from both gens, it deploys. Not sure if apu is running, but I think it won't as the main bus is powered.
If you had a dual at low altitude you would not have enough time to start the apu and therefore pick a landing spot.
Fuel contamination is possible.
CF34 engines are bulletproof and can take a lot of abuse. Not like the old Lears that a blue jay would flame you out.
Very experienced pilots, but everyone I know will tell you of a low fuel situation at some point in their career. You always make it until you don't.
There are so many possibilities off the top of my head, but I know what a gallon of diesel looks like on a bonfire. The wall was pretty burnt up not near resting place so a lot of it may have exited there and burned up and nobody got it on film. I can only expect whatever it was they did a good job saving 3 lives. Any of these problems where they were would have ended in disaster regardless of pilots and maybe much worse.