Marc B did a great job of answering this question. I recently took his approach and wanted to share the resulting code.
<?PHP
$username = "some-username";
$password = "some-password";
$remote_url="http://www.somedomain.com/path/to/file";
// Create a stream
$opts = array(
'http'=>array(
'method'=>"GET",
'header' => "Authorization: Basic " . base64_encode("$username:$password")
)
);
$context = stream_context_create($opts);
// Open the file using the HTTP headers set above
$file = file_get_contents($remote_url, false, $context);
print($file);
?>
I hope that this is helpful to people!