I installed LWP::Parallel::UserAgent and ran your code with and without the commented line. It worked both times.

I modified the output loop so it would just display the content length instead of the whole page content, and I noticed that the offending request actually redirects to one of the other requests in the list, so I wondered if the module is pruning duplicates. I set your $pua->duplicates() call to both 0 and 1, and the only difference it made was that the one request came back "302: Found" instead of "200: OK". I also tried changing the timeout value to a few different things (0, 1, 2, 10), and that never made a difference either.

I recommend you look at your network. Since this is an advertising URL that you're hitting, I wonder if a proxy is helpfully filtering it for you (whether you explicitly go through a proxy or not).

As an aside, I also recommend use instead of require, and I recommend you use strict and use warnings.