We can split words; agree to disagree...
The FX/DX and "Crop Factor" has always seemed a misleading marketing thing to me and I spent a ton of time trying to wrap my head around it.

A DX Sensor is smaller. it uses the middle of an FX lens and all of a DX lens.
An FX sensor is larger it uses all of the FX lens and all of the DX lens, however it (the FX sensor/body) auto adjusts to DX sensor... (uses the DX equivalent/center) of the sensor.

To me... the crop is perfectly clear. The magnification (Crop factor) is not so much that the sensor made the lens a single millimeter longer... it is simply that the smaller captured image has to be enlarged 1.5 times to fill the same print area.

I contend; you are not gaining focal length you are enlarging the captured image more which produces the perception of a longer lens.
have you ever heard the terms Optical Zoom and Electronic Zoom? (also called in-camera zoom, and a few other catchy terms)

It will be difficult for anyone to convince me that a lens gets longer through the process of enlargement of the image.
The focal length of the lens is constant regardless of the sensor, the difference occurs when the image is output/viewed.

Consider it a fact: that when you enlarge a photo on your computer screen, and crop it, the lens in the photographers bag does not magically become longer.
[LOL] Pixel stretching does not and never will effect focal length.

I am anxious to read the arguments that prove a DX Sensor impacts the focal length of any lens: DX or FX.

PCity, sorry you are getting such conflicting, and confusing answers here.
ALL lenses focal length is stated in 35mm film terms, regardless of format or mount. Period.
No matter what the lens says on it, when mounted on a crop sensor body (any camera with a sensor of smaller size than a frame of 35mm film), then that sensors "crop" factor will have to be added in order to get the equivalent field of view when compared to what that lens will yield on a full frame sensored camera, or a 35mm film camera.
NOTHING is ever done to effect the lens' magnification!!! I cannot stress this enough as so many people misunderstand this. A 200mm lens is ALWAYS a 200mm lens regardless. But a smaller sensor cannot capture the entire image circle projected by that lens, the sensor captures a portion out of the center of that projected image circle and that is where the "crop" comes in. The crop factor is the mathematical multiplier to tell the crop sensor user exactly what lens he or she would need to mount on a full frame camera to get the same image view. In your case, and 200mm lens on your Nikon DX body would need to have its focal length multiplied by 1.5 to determine the same image result if using a full frame camera, that being 300mm.
So if you took a picture of a subject with a 200mm lens on a crop sensor Nikon, and a friend took the same picture of the same subject from the same spot, only used a 300mm lens. The two pictures would look identical.
I hope this clears up some of the confusion and answers your question thoroughly.