So I have ran into an issue where a site was using URL's in the file_get_contents function and stopped working on the server. This was also an issue if anyone was trying to do a URL include within a require() or an include(). Here was a solution that I found that worked well with cURL.
$ch = curl_init();
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_URL, $URL);
$data = curl_exec($ch);