OK, I did the following test. I set up a synth (stereo output, no filtering no effects). I put a square wave in a single oscillator and panned it far left. Output was as expected. R channel is totally silent and becomes irrelevant.
When I panned the Channel Tools (hereafter CT) to center with zero width, I got a phantom image dead center. When I expanded the L width control, the output in both channels got about 3 dB louder as I approached the extremes and the phantom center remained dead center. Metering confirmed both were L and R levels were equal at all width settings.
I froze the track and looked at the waveform. As expected both L and R were identical and perfectly in phase. In fact, no phase alteration was ever noticed at any point in this testing (which I think we can all agree is a good thing).
When placing the L control about -15 (halfway left) and initially setting L width to zero, here's what happened. As I expanded the width control, the left channel amplitude stayed nearly constant (increased but only very marginally). The right channel level increased more. Frozen waveforms remained identical in all cases except for amplitude (as expected based on what the meter output was indicating).
So, I'm going to stick to my guns here and say that in the second case (L at -15), increasing the width changed the stereo image, but it did so by moving the phantom center to the right, and the overall level increased. One could produce exactly the same result by leaving width at zero, moving the CT L pan position a little to the right and increasing the level slightly.
In a situation like this, we've got two identical audio streams in L and R - identical except for amplitude that is. As we increase/decrease either side, the perceived panorama position will naturally change. But if the two waveforms are identical other than amplitude, that's all that changes. That implies that I could produce two exports, one using CT width manipulation and one where I just altered pan and overall output level and I could achieve two exports that are identical. And if this is true, then there's no width manipulation actually happening. Changing CT width is just moving the panorama position and messing with amplitude. Thus, CT width is not doing what it's claiming to do.
Anyway, that's my story and I'm stickin' to it.