Take a globe. Turn all the lights off in the room. Shine a flashlight at the globe directly at the side with the north pole leaning toward you. Does the north pole on the globe always appear lit as you spin the globe on its axis?

You're confusing midnight with night time. Midnight is just a function of the clock. Night time generally equals darkness in most peoples minds. If the sun is shining at midnight, there is no darkness at midnight regardless of that particular time being called "midnight".

Midnight sun simply means that the sun is out at that particular time of day.

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Spock Jenkins of the Vulcan Jenkins'.