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A few points
You probably do have saturated images if you have pixels at 64000. I assume that the camera has antiblooming and probably this is stopping the pixels reaching ~65000.
Flat framing will change these levels and can make some increase. A flat is divided into the light frame pixel by pixel.
For the median value of your flat, those pixels will be divided by 1 resulting in no change. In dimmer areas of the flat the pixels will be divided by a number less than 1 resulting in an increase in the count of those pixels in the light frame.
The reverse occurs in the highlit areas on your flat.
Think about what happens when there is dust on your CCD. The counts under the dust mote will be lower than expected resulting in a dark dust bunny on your image. You take a flat frame and this shows up the dust bunny. When you apply flat it brings the count of the pixels under the dust bunny up to the same as the surrounding region therefore making the dust bunny disappear.
As to saturated pixels. Does it really matter? For me it does if I am doing photometry but for pretty pics it is pretty hard to not saturate bright stars and still get enough signal in extended objects to see them.
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