Curious. On a test machine I tried running updateniceurls.php and then republishing the node from ezwebin. Then, on attempting to view a page 3 levels down, Firefox reported that "The page isn't redirecting properly. Firefox has detected that the server is redirecting the request for this address in a way that will never complete."
The admin interface showed the node in question (depth=2; the root node for one of the two sites on the installation) had been given the URL alias for the root node (depth=1, node 2). Ran updateniceurls.php again to no effect. Then I republished it again from the admin interface; problem solved.
Could I have something set incorrectly, or might this be bug report material?
By the way, I'm running 3.10, on a site that had started at 3.9.4.