This is a good explanation, as was the earlier explanation of the potential effects of decoupling.
I hope that Adam won't mind if I expand on his Audyssey explanation a little. Audyssey's creator points out that unlike older graphic equalizers that affected the frequency response at the source, Audyssey makes corrections in both the frequency domain and the time domain because it measures and corrects for frequencies at the main listening position. So, to some extent at least, it can influence the effects of room modes and room reflections. Unlike a graphic equalizer, it makes those corrections automatically, so the more that we can do to present the EQ software with a favorable room condition, the better. Sub (and speaker) placement, and other factors can help with that, as can distance tweaking and other measures, post-Audyssey.
With respect to fixing peaks and dips, the Audyssey software is capable of adding 9db of boost to a dip, but has the ability to reduce a peak by up to 24db. One of the reasons for that disparity is the additional power required to boost dips, as Adam pointed out. The other reason is that where severe cancellation is involved--for a room null--no amount of boost will influence the null. Nulls show up on FR graphs as very deep V-shaped dips. They can easily be 30 or 40db deep, but are typically pretty narrow in width. More normal dips in frequency response tend to be shallower and have more rounded outlines. Audyssey can help with dips (up to 9db deep) but can't help at all with genuine nulls.
Edit: I decided to add to my post by saying that Audyssey can't really tell the difference between a dip and a null. Or, if it can, there is no evidence that the software reacts differently. So, in a situation where a sub is chuffing, for instance, it is conceivable that Audyssey is adding boost to a dip, or a null, in a way that adversely impacts the available headroom of the sub. That's one of several reasons why good initial sub placement can be important, not just with respect to general frequency response, but with respect to subwoofer headroom as well. Like any tool, Audyssey is primarily useful when properly employed.