with someone means
Accompanied by
or
agree with or support someone
It sounds like the video is saying (link with a time stamp where I am talking about)
A friend of Grylls who was with him at the time told The Guardian: "I look back and think of him in the body brace after that horrific parachute fall, and it's incredible that he survived it. Then to look at what he has achieved since then, I'd never have thought it possible."
Does "with" here mean the friend and Grylls parachuted almost at the same?