I have own several eels, and have spent tons of time with them.
Was very clear to me the difference of both videos.
The second video clearly shows those people are completely idiots, they were teasing the eel with food, making it chase it.
Your 100% idiot teasing any animal with food, that can physically damage you.
If you noticed how first diver handle the animal she was watching his reaction before she reacted. For those that do not know her, She been making films for over a generation. She has been diving to that spot for over 20 years.
I would never say its 100% safe to handle a very dangerous animals.
There are ways to handle animals, and more importantly to understand their body language, so you can react according to the situation.
Please do not judge one video, someone that has spent all their lives in the ocean against some weekend rodeo idiots.
She should be praise for showing the world, how a top predator can be handle in a way, that shows a different side to them, an animal that enjoyed being touched by a human being.