The long distance to the Sun mandates long exposure times. The New Horizons spacecraft needs to be relatively stable and its pointing accurate throughout these long exposure times.
New Horizons does not have a scan platform. The cameras and other science instruments are fixed with respect to the vehicle. The satellite has to turn as a whole to keep the its scientific instruments pointed at Pluto. New Horizons also doesn't have control moment gyros or reaction wheels. All attitude control is via attitude thrusters.
The vehicle has to rotate by 180° from well before closest approach to well after closest approach. With a somewhat remote flyby, this 180° turn is spread out a bit. With a close-in flyby, this 180° turn has to happen rather quickly, right at flyby. The constant on/off thrusting that would be needed for a very close approach would do significant damage to the quality of the close-in imagery. There's little value to a close-in flyby if all that one sees is fuzz. A close-in flyby would also require considerably more fuel than a more remote flyby.
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