Here is a critical point: with a left hydraulic system failure, you have no nose wheel steering.
You can’t steer. You have only differential braking to steer while on the ground.
Flaps 20 landing with a tailwind at high altitude = a lot of speed on the ground. A LOT of speed.
The crew may, emphasize may, have chosen to use max reverse on the right engine (which was not available on the left engine with a left hydraulic system failure) to shorten the landing roll.
But with no nose wheel steering, at low speed, where the rudder is no longer effective, that thrust differential (idle forward on the left, full reverse on the right) could cause directional control problems, pulling the airplane to the right.
That would require full left brake (the one that was smoking) to try and keep the airplane from pulling to the right.
Juan speculates that the crew was trying to make the turn off.
My suspicion - full reverse on the right, with no nose wheel steering caused a low speed loss of directional control.