I'm pretty sure you can send your own username and password down the pipe via AJAX with the web services. Obviously, I've never tried b/c I know the security ramifications of doing so, but a username and password parameter is available to your with the AJAX request. You *could* override the SPService default authentication (current user) by using the $.ajaxSetup() method.
I am absolutely not saying you should though. The username and password will be sent down the pipe in clear text, which is never a real good idea...
Cheers,
Matt