Very simple
If this company, (it's obvious from the video who it is!) allows B757 to reverse using TLs, then the crew are in the clear.
If not, then the crew (captain?) is a cowboy/cowgirl!
As I said. Very simple.
What if no book of authority mentions it?
Two distinctly different attitudes to aviation are,
- Everything is allowed, unless specifically prohibited
and,
- Nothing is allowed, unless specifically approved