For one thing, it assumes that only a small fraction of the image sensor's surface is actually capable of detecting light, which would make it very inefficient. Typical consumer digital cameras can capture over 30% of the incoming energy, and presumably New Horizons' camera can do better, being specifically designed for a low-light environment.
More importantly, no atmospheric "diffusion" is required to spread out the incoming light, because it's occurring anyway through diffraction at the camera's aperture. The angular resolution of the LORRI camera is specified as about 1 arcsecond, which is comparable to the atmospheric seeing conditions on a relatively clear night on Earth.
This is exactly the same effect. There are probably not any stars of high enough magnitude to be visible on the same exposure with such a bright object. In fact, there are definitely not: otherwise, we would see them on the image.
For more proof, check out some earlier navigation images taken by New Horizons as it approached pluto, greatly overexposing Pluto and Charon in order to see the stars around them: https://twitter.com/NewHorizonsBot/status/615264675975065600
It's difficult to imagine Pluto, being so far out, being "bright," but remember that light intensity falls off at an inverse square rate with distance. New Horizons being so close to pluto, it's actually an extremely bright object relative to the stars behind it.
In fact, NASA did a fun twitter experiment where they gave people the exact time at their location on Earth when it would appear as bright as noon on Pluto. You can see many resulting images here, illustrating how bright the Pluto surface might look were you standing on it: https://twitter.com/search?q=%23plutotime
See how many stars you see near pictures of the moon: https://www.google.com/search?q=moon&tbm=isch
Most photos from space don't capture stars unless they're trying to, because whatever object they're photographing is sufficiently bright to blow out any stars.