Sorry, I don't understand what you just said.
I had read the first few chapters of the 101 on strobist, and just now scanned the rest, and I can't find any reference to 2 exposures or anything about that.
Doesn't the shutter speed work with flash the same as without flash ? In other words, say you are in AP mode. If you use flash, the camera will know there is more light coming, and accordingly speed up the shutter, and that's why you would have a clearer picture ?
It's two exposures. You get the exposure from what ambient light hits the sensor and the exposure from the flash. This is assuming one is using manual mode and the camera isn't doing the exposing for you.
Like say you're inside. If you shoot at ISO 100, a shutter speed of 1/250 and an aperture of f/9, you'll most likely get a black photo, unless your lights are extremely bright. If you're using a flash, it's what exposes the scene in that case.
So ambient light creates no exposure because of the settings. The flash is what lights things up in this case. Small speed lights like the Canon 580EX can has flashes as short as 1/15000 of a second. That's how long the light last from beginning to end. That's what creates the exposure, provided settings are right.
Now, if you're shooting inside and you're shooting at ISO 100, a shutter speed of 5 seconds, and an aperture of f/9, you could probably get a properly exposed picture in the same situation as above. The problem is that a shutter speed of 5 seconds is not enough to freeze motion, in fact, it's probably not enough to show anything that moves infront of the lens. You may get trails, but that's it.
If you have a flash with the settings set to match the camera settings and you fire it with the above settings, you're going to have the ambient exposure of the room, along with the exposure created by a flash. So if you catch a cat moving infront of the frame with a flash that has a duration of 1/15000, it would be like you're using a shutter speed that fast.
In fact, you can do multiple exposures. Each time you pop a flash, it will show what ever it lands on, provided it's power is set to match your camera settings.