It looks like there is a piece of code in qa-page-question-post.php that blocks attempts to remove the category from a post:
if (!isset($in['categoryid']))
$in['categoryid']=$question['categoryid'];
When setting the category id of the question to "No category", the script sets $in['categoryid'] to NULL, which I guess is the equivalent of it not being set, so the script resets it back to the original value. That's what seems to be happening, anyway.
I guess it's not often that you want to set the category to "No category", but it seems a little odd to not allow it intentionally, and it's making trouble for testing the Categorizer plugin.