I've managed to work around the problem by using a custom field called page-order associated with my pages and by setting order_by to numeric and meta_key to page-order. That seems to work as I expected. Oddly, I first set order_by to custom and it didn't work as expected.
Not sure whether this is of any help or not. On the one hand, I really want to get the previous/next links up and running properly on my site, but on the other hand, manually setting a custom field each time I create a page isn't ideal either ... so I'd really like to try and get this problem, if it is a problem, solved.
-Gary