Incorrect, line training??
What about line trainers without TRI/TRE?
When does somebody become legally qualified? Once they have finished their line training?
Line training is an internal company process (essential though). That trains a qualified pilot in the company procedures and enables the pilot practice what they have learned under the supervision of a more experienced Captain.
Line trainers are not providing any training towards a licence, rating or to a pilot who does not have the required take-off and landings in the previous 90 days.
The pilot is licensed to fly the aircraft and act as a member of a crew as soon as they get the rating on their licence.
The company usually is a bity more cautious and limits them to flying with a line trainer until they pass their line check. Some companies still restrict pilots who have just passed their first line check to flying with the more experienced people who sit in the other seat.
What you have to rememebr is that there are many cases where there will just be two crew on an aircraft that requires two crew and for example the FO may not have passed their line check. In this case the Capt will at least be a line training Captain. In that case what happens when the Captain needs a physiological break during the say 8 hour cruise? What if they think they can't leave the seat and as a result become incapacitated?
One of the best examples I can think of is the good old 3 take-off and landings in 90 days. Most companies have more strict requirements. If the other pilot is within the 90 days but outside the company requirement they can fly with a line training Captain. As soon as they pass the 90 days then they are no longer legal unless they can (between 90 and 120 days) fly with a TRI on a revenue flight.
Beyond the 120 days they have to either go to the sim or fly the aircraft empty.