general_audiologist,
All this technical talk notwithstanding, here's what really happened...
One day, Bubba was reared back in his La-Z-Boy, drinking beer and listening to his stereo and it occurred to him... "Unless my speakers are exactly the same distance from me, their sound won't get to me at the same time. I know how fast sound travels, so if I measure how much closer one speaker is than the other, and can delay the signal appropriately to that speaker, I could make the sound hit my ears at the same time".
After a couple more beers, he figured he could do the same thing to "match" all speakers in a surround system. Then he ran out of beer, and cracked open the moonshine. After a couple swallers, he realized he could also measure the volume of each speaker, at his chair, and match their volume so the closer speakers didn't sound louder. (He didn't realize this could be useful in smoothing peaks and valleys caused by room geography and furniture, but heck, it's only Bubba.) Then he passed out and slept. But while he was sleeping, he dreamed about checking phases too.
So that's the real story behind Audyssey. You can see there is nothing there about making a bad speaker sound good. It's only about trying to mitigate or "balance" effects from the environment that exist between the speaker and your ear(s).
Dr. Toole,
You sound like a pretty good guy. Thanks for trying to help. But I gotta say, you sure use a lot of big words.