I created a variation from your example to show it happening. http://jsfiddle.net/4pjdj/.
You can also see it at http://hiring.snagajob.com where it makes a call to dev.visualwebsiteoptimizer.com/log_hit.php if it's your first time on the site and to dev.visualwebsiteoptimizer.com/log_clickmap.php every time you click the page after that. Both calls cause the active variable to increment, but not decrement.
It's my assumption that the complete event should be called even if the response type is incorrect. I believe that would decrement $.active correctly.
Also, I understand your point about the active property not being a documented feature, however, it's the core of our automated test framework which uses it to ensure the page has fully loaded and is not in the process of making any additional ajax calls before it starts running tests on the page.
Thanks again for your help