Sitigeltfel....Do you know exactly where the photo in your post was taken??....If it is where i think it is,a full set of engine guards are provided at this location and SHOULD have been used!!.
As for working on engines whilst they are running,yes most engineers have probably done this on many occasions,but i have never known anyone do this when the engine is above idle....Even at that setting on a Trent/GE90 it is a little disconcerting,so good teamwork/trust is vital to say the least.
I cannot ever recall seeing anyone on a "tethered line",so cannot comment on this approach, but in my opinion,it does seem to add an extra hazard to the proceedings.
Condolences to all involved.