Since you can see stars near the moon, you should be able to see stars near Pluto, which is less bright. More likely, there are no stars in the (very narrow) angle of the camera.
This is exactly the reason. Properly exposed with a camera, you cannot see stars near the moon.
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
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 :)
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.
