Files an a server may be considered "private".
However, when you make those files available through a web server, you make the "public".
You then have the ability to limit the access to those files through any one of a large number of techniques to make them private again. Now if there were evidence that they tried (and failed) to use one of these techniques or that the teenager in question deliberately circumvented these techniques, then you would have a point.
One (not particularly good) way of limiting access to files without verifying identity would be to create a hash (say using the requesters email address and the request ID) and use this in the url to access the document (similar to how google docs implement sharable document links).
If they had done this, then perhaps you could legitimately claim that there was evidence of intent to restrict access.
An incremented ID is the opposite. It is a sign that you wanted people to be able to easily predict the correct url to download the next file from. Using an incremented ID is in fact evidence that this information was intended to be public.