Kevin, there are several reasons to background to be dark. Imagine, background locates far from your subject, beyond the flash reach...
Yes, people need to stay awake during physics class....
Light falls off at the rate of the square of the distance from the source.
With low light indoor shooting, that translates to......
Subjects at say 5 feet from camera, nicely flash exposed.
End wall of room say 10 feet from camera, nicely underexposed by 2 stops.
The 1 stop underexposure distance would be at 7 feet from the camera. That's 5 feet multiplied by the square root of 2.
If there's some ambient light, then a slower shutter speed is called for to try and use that to lighten up backgrounds for flash shots. But then of course subject movement and camera shake problems enter into the equation.
As for light falloff, it's just like balancing studio lights, be they flash or floodlights. Light A at
x feet from subject, same strength light at 2 times
x feet away contributes 2 stops less light. To get 1 stop less light on the subject for not so dark shadows, move the light to 1.4 times the other light distance from the subject. (1.4 being about the square root of 2, and 2 is the difference in light due to 1 stop change). Of course any background light on a backdrop needs to be same strength and in the same range of distance from the backdrop to contribute the desired exposure to the backdrop.
You can learn a huge amount about lighting by using two identical strength bendable desk lamps and use a tabletop setting like an ornament as a subject. Muck about with angles and distances of the lights to see the effects change. Use a third light to illuminate some bland backdrop, like a sheet of cardboard behind the subject. Experiment with spacings of the lights to get an attractive effect. The effect on the exposure is always more severe than the eye sees, shadows get blacker more quickly, so always judge from shots taken, not what looks good to the eye.
Anyway to avoid those dim backgrounds for indoors flash shots, go buy a big 4xAA battery flash and use it in bounce mode off the ceiling. Suddenly you get fantastic flash shots that can look completely non-flash if done carefully. Some possibilities in my flash list here...
http://homepages.ihug.com.au/~parsog/panasonic/11-flash.html#flashlist
Regards.......... Guy