Just to clarify the article: using AJAX should work fine, but only if the page you’re launching the AJAX request from is on the same domain as the URL you’re sending the request to. Doing AJAX requests from other websites is not possible.
So if you have the script at website example.com/log.php, you can do AJAX from example.com or example.com/forum/topic/123.php, but not from example.net.