In the boat involved in the electrocution, the AC and DC wires were also not initially connected. Likely the AC wire was underated for the application and got hot because of a big load (like air conditioning or maybe running two space heaters or??). The AC and DC wires were very near each other and the heat of the AC wire melted the insulation and then the AC hot wire was imposed on the DC. Even if this boat had GFCI protection, if the place were the wires fused is before the GFCI outlet, the GFCI wont do anything. GFCI only protects things plugged in AFTER the GFCI circuit.
In your case, chances of a problem are very small.. but it is exactly the sort of sitution which could cause this sort of problem. If your AC extention cord was underated (looks like its OK) and got very hot and melted the insulation for example from running an air conditioner or two space heaters, the AC hot wire could connect to either the solar or generator wires effectively imposing 110 VAC on your boat DC ground. If your outboard is connected to the boat ground for either electric start or an alternator, your outboard would be at 110VAC potential and if its in the water, dangerous for someone near it also in the water.
I really dont think you have much risk at all.. a series of unlikely events had to come together for the referenced accident.
Dont really mean to use your picture as an example but I just wanted to point out that running AC and DC wires close together like that especially before GFCI protection is generally not a good idea. Im not sure there are standards on this sort of thing but making sure AC and DC runs are seperated before GFCI should be one of the standards.
FYI, I do use a space heater during the winter and at 1500 watts, the extention cord can get a bit warm..I really should get one rated for higher current.
Edit - also seeing that your home outlets are all GFCI, you would be protected. Similar to a marina which has GFCI outlets. If the marina outlet would have been GFCI, as soon as the outboard got charged, some of hot AC current would have flown to ground through the water and created the imbalance in hot and nuetral lines which trips the GFCI. The marina outlet would have tripped removing AC to the boat and the accident would never have occured.