ja sam imao isti problem (tj. request), i isto sam pitao to na forumu, evo ti link:
http://www.devprotalk.com/showthread...hlight=youtube
na kraju sam to resio klasicnom kradjom

evo ti kod koji sam koristio, u nadi da ce ti dati makar insight u jedno resenje.
*note da je ovo
samo za youTube..*
Kôd:
// jel' ovo uopste youtube embeded video?
$parchePos = strpos($nekiEmbededLink, "www.youtube.com/v/");
if ($parchePos === false) {
// ako nije youTube, postavi neki default.. bla..
}
else {
$youtubeID = substr($nekiEmbededLink, $parchePos + 18, 11);
// KRADI!! :D
$ch = curl_init ("http://img.youtube.com/vi/$youtubeID/1.jpg");
curl_setopt($ch, CURLOPT_HEADER, 0);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_BINARYTRANSFER, 1);
$rawdata=curl_exec ($ch);
curl_close ($ch);
$fp = fopen("userPhotos/{$article_id}.jpg", 'w');
fwrite($fp, $rawdata);
fclose($fp);
}