You can get so into the technical stuff you can even arrive at an incorrect conclusion like something is not useful.  From a practical standpoint everything is useful.  Channel Tools is a very useful plugin to have around. As someone who mixes a lot I tend not to think of it as a device for increasing apparent width but much more often for me anyway decreasing width.  It is also good for fine tuning levels of both L and R channels.
 
I am working on a mix now that is big and complex and quite a lot going on right across the stereo field.  The client supplied some extra pad like tracks.  They were nice musically but very wide.  Due mainly I would so say to the processing that was on the last stages of either a virtual or hardware instrument.  (and also in programming of course)  When put into my existing mix I felt it was just out on the sides too much.  I wanted some stereo but not so wide and I wanted that whole sound to move to the left slightly.  Channel Tools did an excellent job.  Once it got out of the way of the sides and moved to the left a little it became easier to hear.  Maximum illusion, minimum voltage. I was able to turn it down. 
 
I got a bass part that was also very wide (some wild panning) and it too did not sit well being so wide with a wide mix so I planted both channels in the centre and it too became clearer and louder, able to turn it down and still hear it etc..
 
I have also had the situation where I either recorded or received a nice pad part in a piece. It was stereo and sounded nice at the time. On further listening I discovered it was not stereo enough. It had a little width.  It was having trouble being heard.  There are better processors than Channel Tools out there that will widen a sound like this and put it well into the sides and well away from the centre.  And doing it all without using delays but much more interesting techniques that you don't need to understand.  All you need is to understand what they do to the sound.  What a good widener will do will make the pad sit well out away from the centre so it becomes very clear and easy to hear.  I was able to turn it down again. 
 
I check all mono compatibility by summing L+R and listening to a small single point source mono speaker.  The better more interesting widening processors play well with the mono check.  Once you start turning the polarity of one side of a stereo image upside down is when the mono test fails badly. eg some parts disappear all together!  That is a horrible effect in most circumstances.  I prefer to leave that alone.
 
It is also very handy to be able to flip the polartiy of one side of a stereo signal too.  I have used that correct a bad stereo effect that must have used the same technique.  And it is also nice to be able to use the delays on one side.  For a slow moving pad I have been known to add 100 mS or more to one side.  It creates a lot of width due to the time distortion going on.  And it sums great in mono too.
 

Hi Geoff,
 Thanks for the added info.
 
 BTW, It occured to me that the change in waveform shape as displayed in the screen shot I posted is probably the result of additive synthesis of the two different frequency sine waves as they overlap due to the "widening".
 
 

dmbaer
So, my original question was really whether or not there was something else going on that the CT documentation wasn't telling us, such as the use of a Haas delay to produce a faux stereo quality - two versions of a single channel's content.  Once you had that, then you should indeed be able to produce a sense of width.

It can do that sort of thing using the Delay parameters.

mike_mccue
I have appreciated the discussion that your question inspired.

+1

dmbaer
The width controls next to them are illusory, since they are just altering the pan position beneath the covers.

This is exatly what the width does as I understand it, but it does it from within the control. It's as if you could turn the pan bot on the track to increase the intensity of one side or the other before the signal enters the plugin.
 
As far as I can tell, that's what it does exactly. It allows you to emphasize the audio entering the plugin on one side or the other. 

I worried about mono compatibility for a few seconds and then thought "I like how it sounds" and forgot about worrying.
 
A casual supposition is that it is not much more of a delay than you hear with ORTF, and that collapses without to much concern.
 
FWIW, I am just speaking of S-1 Imager, not the Shuffler, which I have but will admit I am not familiar with.

I guess I just don't know anything about "shuffling" or where it is on the S-1 Stereo Imager GUI
 

 
The thing I like about S-1 is that the result I am describing results from simply turning the rotation slider. A single adjustment and I hear a distinct difference.
 
This illustrates what I hear:
 

 

 

 
I've posted links to these screen shots in the past and found that many viewers don't have the attention span to notice the salient detail that it clearly illustrates, but I'm confident if you look carefully you'll see what I am talking about.
 
Drew recognized the detail and once commented that the time shift is very very very small, and indeed it is. I find it remarkable that this very small difference makes, in my opinion, a dramatic difference to what I hear.
 
I'd like to emphasize that I heard this effect first and then after appreciating it for a year or so, I stopped making music long enough to go run some tests and figure out exactly why I enjoyed what I was hearing. I thought it was pretty cool.
 
 

Hi David,
 I have to make a confession. I have made a mistake of sorts, and I am going to admit it.
 
 I just took a moment to replicate the results shown in my screen shots on my current DAW and I could not replicate my own results!!!
 
Now, before people say "ah hah MQ's an idiot" let me explain further.
 
I was so distraught to learn about this mistake that I fired up my moth ball DAW and found the original test I had made.
 
Here's what I found: On my old DAW I am running an ancient S-1 Imager, version 5, and it does indeed exhibit the characteristic I am describing. So, I went to my new DAW and confirmed that I had the exact same settings in S-1 and sure enough the timing on the left and right channel match perfectly with the new version (well to be honest it looked like the right channel was a single sample, at 44.1kHz, late, but that could just be the wave form drawing).
 
For my current DAW I purchased a Native Power Pack license because I find I only use 2 wave products S-1 and De-esser. So on the current DAW I am running Waves version 9.01.
 
The two S-1 versions have significantly different output. I don't know why, but I just confirmed it by running both DAWs back to back.
 
Anyways... now I know why a lot of folks can't hear what I say I've been hearing for all these years...
 
...but I have also confirmed to myself, once again, that expectation bias is extremely powerful because I had not noticed the fact that there was no longer anything to notice.
 
So there it is. I feel foolish at this point but I'm willing to stand up and say "wow"... I think I'm gonna go make some music. :-)
 
 

My favorite of the Waves spacial tools is the PS22 XSplit plugin. I know it's primarily a mono-to-stereo processor but it can also widen (and rotate) stereo tracks as well. I'm definitely still an audio amateur, but to my ears it's the most authentic (and mono-compatible) widening technique available to me. It spreads the frequencies across the stereo field from top to bottom in a wave pattern (you can adjust from a sine wave to a square wave), which collapses to mono almost perfectly.