When is a pilot performing a published instrument approach not authorized to perform a procedure turn?

The correct situation in which a pilot is not authorized to perform a procedure turn while executing a published instrument approach is when receiving a radar vector to a final approach course.

In this scenario, the pilot is typically being guided by air traffic control to align with the final approach path. The use of radar vectors implies that the pilot is directly following ATC instructions, and performing a procedure turn could conflict with the clearance to proceed directly to the final approach segment. Procedure turns are designed to be flown only when specifically authorized under the approach procedure, and when receiving radar vectors, the controller has already designed a safe and efficient routing that bypasses the need for such maneuvers.

The other options describe scenarios where a procedure turn might or may not be appropriate based on individual circumstances but do not specifically negate the authority to perform a procedure turn like receiving radar vectors does. In all, the use of radar vectors indicates that ATC is providing guidance that eliminates the necessity for a pilot to execute a procedure turn, focusing instead on efficiently bringing the aircraft onto the final approach path.