Quite simple really. Let's break it down. Speakers are designed to measure "Flat" in groundplane or anechoic space. That is how they are built and tested. Now there are many out there that are "Voiced" to add a sonic signature that that manufacturer deems prefereable to the end user and/or their design/listening engineers. But for the sake of simplicity, lets take a high quality speaker, that is simply designed flat (JTR, Seaton, Danley, etc). The speaker once placed in a room, ANY room, will be far from flat. Did anything change with the speaker itself? NO!!! So you could already say the sound has ALREADY been influenced after it has left the speaker.
So what does audyssey do? DSP aka Digital SIGNAL processing!!!!! It reads the response that the room has helped to create at the MLP. It takes this response, and inverses the SIGNAL where it needs to to correct for these room reflections and the end result is a far from flat response at that point coming from the speaker. It then reacts with the room around it and ends up yielding a flat response IN ROOM.
That's impossible as I see it. Even if Starfleet Command themselves had designed the Audyssey algorithm and given it miraculous properites for manipulating the signal inside the AVR, once the sound has left the AVR and left the speakers, that nice manipulated sound starts bouncing around the room again. Yes, as you say, the sound post-manipluation as it leaves the speaker is possibly far from flat because it takes account of the room influences when it was first manipulated - but once it leaves the speaker it starts to reflect all over again - the 'Audyssey sound' is now reflecting off the walls and it would need yet further correction which of course it cannot get (maybe if the filters were created and adjusted in real time this would be possible, but I still doubt it). There is also the pesky little business that nobody has ever produced a measurement that shows any correction in the time domain, other than as a by-product of manipulation in the frequency domain.