Perhaps no significantly bright stars. I find it unlikely that there are zero stars in that field of view, especially since the probe and planet are most likely roughly in the plane of the galaxy.
This is basically heresy, but what I've been told is that imaging stars from space is actually more difficult, because there is no diffusion of the local atmosphere to help increase the perceived size of the point light source.
If you're saying that the images of all of the point sources manage to "miss" the image-sensing regions of the camera sensor, then I seriously doubt that explanation.
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.
Ah yes it is reasonable that several other characteristics make the sensor less likely to register photons from the field of view here. (The sensor/lens could also have some spatial frequency response characteristics that filter out non-diffused stars). I don't find it reasonable that there are no stars in that field of view though :)