Registrar's private WHOIS services are only for domains registered thru them. You can't register at Yahoo and get Namecheap's WHoisGuard. If you did it through a different service it would be the same as getting your friend or the guy down the street to use his contact info and hold the domain for you.
Hmm...so what is the best way to protect one's identity without getting WhoIs privacy and still complying with rules of registrar?