Mixing flash with ambient lighting offers the photog, a dramatic control over the mood of the photograph. Nothing is right or wrong in photography. It is an art and well there is always creative license to break rules. However understanding technically the rules help us understand the side effects of breaking those.
It is important to remember that in situations where the lighting is a combination of flash/strobe and ambient provides us an ability to control each with the help of camera settings. In short, the shutter speed controls how much ambient light hits the sensors whereas the aperture or f/stop value controls the strobe light hitting the sensor.
A typical use of these values is to underexpose the background using a fast shutter and maintain a desired f/stop to control the light falling on the subject. More on the topic below in the Mark Wallace video.
Btw if you are a photographer who wants to improve and have not started viewing the Adorama TV's Mark Wallace tutorials, you are missing out on great info. Here is the link to an episode where he talks about what we discussed above - http://bit.ly/rEvU3m