I doubt that the category information is available to the product page in the default installation. You can use the tip I told you about in post #6 to see the smarty variables that are available to you. If it is there, you can update the template to display the categories.
If the categories are not there - you are going to have to write your own query to get the information and add that to the product.php file. I think you need to query the _products_categories table and find all categories for the productid.
If you understand the code
in this thread (the sql query and the php), the concept is similar to what you want to do. You should be able to add an array with the categories to the $products array.