The fallacy in the quoted sentence is that the relativity principle of SR only asserts the equivalence of all inertial frames of reference,5 and B does not remain at rest in any one inertial frame throughout the trip. The outgoing inertial frame in which B is at rest for the first part of the trip continues to move in the same direction forever. During the second half of the trip, B is at rest in an incoming inertial frame and moving at a high speed relative to the outgoing frame. A better understanding of the situation comes from simultaneity considerations in the three frames of reference.