To be a little more specific, I do know this about AjaxExtended's solution. Imagine three servers, A, B, and C. You install server side code on B. Once that's done, you can include Javascript on web pages on server A that will allow these web pages to access Server C. The part I understand is that server B works as a proxy to server C (using PEAR). Server A creates the page that includes Javascript from server B. Then it talks to server B (I don't know how) and server B uses PEAR to go out to Server C and returns the result to the web pages that were created by Server A.
So the effect is that server A pages can talk to server C - which is a function that is expressly prohibited by the XMLHttpRequest methods, as you said.