not true at all I'm afraid, all fcc TL drivers sign and drive 377's.
Well I know one driver who I worked with on southern who was told by doctors to stop driving 377s. Southern refused to allow him to continue working as a driver if he couldn't drive all required traction and so FCC took him on allowing him to work 319 only.
This was a number of years back so things may have changed since but I know he did move to the TL in order to escape 377 driving.