The power split device requires the engine to be running to prevent overspeeding the motor-generator. The max speed on the MG is 10,000 RPM which equates to ~40MPH. Anything over that requires the engine to spin, although, as lakedude pointed out, there are times when there is no fuel to the cylinders so it is a very smart vehicle in that aspect.

My 4WD
Wife's 4WD