Let me explain a little bit about the 502 error, because the chances for everyone to access the page with the link (and therefor the iOS Limited Beta) are the same, regardless of your ping etc.
There is a system in place that works similar to an elevator. It allows x amount of players to download the page at once. Once someone is finished downloading the next person is allowed to download it. So how does it decide the next person who is allowed to download the page? It picks the first person who asks for the page to be downloaded after someone has finished downloading the page will be able to start downloading it.