I'm also in Europe were the lawyers don't dictate life just yet.
Either pilot in my outfit is trained to perform the task described.
So pilot flying controls pedals, yoke and thrust levers.
When either pilot see, hear or feel something unusual they yell "STOP".
Pilot flying than performs the RTO.
I'm happy with that procedure cause there is almost no delay and Pilot Flying can feel a yaw momentum better/faster. The assumption that a F.O. will screw it up and a P.I.C. won't makes me wonder who you guys have to fly with. From all the procedures we learn this is not the most difficult one. Sure it is critical, that's where training comes in play.
Airlines and/or people will always disagree and luckily we can discuss it at length. But in the end we will do what company procedures dictate. Cause a. they pay our bills but more importantly b. that's what the guy next to you expects you to do !!!
(P.S. I had an actual one two months ago and it worked fine.)