No, Kiernan, at work I do not "free climb" telecommunications towers: rather, I use fall-protection equipment such as a full-body harness with lanyards and rappel lines.
Here for example I am on rappel with a lanyard on a backup line (January in Puerto Rico):
Here (today in Juneau, AK) I am on step pegs with a grillon, a lanyard, and a lad-safe.
Thanks for taking an interest in my occupation! The video you linked to is a an example of unsafe climbing, and it caused a lot of discussion
when it came out.
Luke, we will have to see about setting you up as an assistant, but if so, I'll require you to climb using fall protection; the Rocky Mountain PBS tower on Lookout Mountain needs a structural upgrade, and I hope to work on that job if/when it comes in!
Outside of work, however, you may in fact find me free soloing the flatirons, or doing a handstand near a crevasse on the Mendenhall Glacier: