Wrong (in my experience). I used my LTSB 241 voucher on my Avios.com account and booked for my daughter and MIL. For the AmEx 241 on BA.com I understand that the cardholder has to travel, but not for the LTSB card. Whether this is a loophole on Avios.com or not I don't know - the terms do say that "9. The ‘Companion’ must travel to the same destination as the cardholder and be accompanied by the cardholder in order to take advantage of the Companion Ticket."

In my case if I got challenged I would say that I am travelling to the same destination and am accompanying those travelling, just in a different class with a ticket obtained through a different scheme!