Cross-site AJAX requests
The post marked as the answer is erroneous: the iframes document is NOT able to access the parent. The same origin policy works both ways.
The fact is that it is not possible in any way to consume a rest based webservice using xmlhttprequest. The only way to load data from a different domain (without any framework) is to use JSONP. Any other solutions demand a serverside proxy located on your own domain, or a client side proxy located on the remote domain and som sort of cross-site communication (like easyXDM) to communicate between the documents.
The fact that this works in IE is a security issue with IE, not a feature.
Unfortunately cross-site scripting is prohibited, and the accepted work around is to proxy the requests through your own domain: do you really have no ability to add or modify server side code?
Furthermore, the secondary workaround - involving the aquisition of data through script tags - is only going to support GET requests, which you might be able to hack with a SOAP service, but not so much with the POST request to a RESTful service you describe.
I'm really not sure an AJAX solution exists, you might be back to a <form> solution.