The focusing system used by the camera when you are using the viewfinder is an independent system from the focusing system used when you are using Live View.
Each system is designed and operates completely separately from the other. One works when the mirror is flipped down and the imaging sensor is "blind". The other works when the mirror is flipped up and the dedicated PDAF (Phase Detection Auto Focus) sensor is "blind" along with the viewfinder.
Both systems have relative strengths and weaknesses compared to the other. You've discovered one of the strengths of Live View and one of the weaknesses of off-sensor based PDAF systems.
Most DSLRs, even high end ones, have relatively limited areas near the center of the frame from which to select AF points. This is governed by the shape and size of the hardware used to make the dedicated PDAF sensor array. In fact, the dedicated PDAF sensors in most larger sensored cameras are more limited to areas near the center of the frame than smaller sensored cameras. If one uses the same dedicated PDAF sensor array, the same angular amount of coverage will stretch over a larger percentage of a smaller imaging sensor than the same angular amount of coverage will spread over a larger sensor.
Cameras with imaging sensor based AF systems usually allow selecting focus areas that cover more of the total frame. This is allowed because the hardware used to detect contrast is embedded into the imaging sensor itself.