The response from server is JSON String format. If the set dataType as 'json' jquery will attempt to use it directly. You need to set dataType as 'text' and then parse it manually.
$.ajax({
type: 'GET',
dataType: "text", // You need to use dataType text else it will try to parse it.
url: "http://someotherdomain.com/service.svc",
success: function (responseData, textStatus, jqXHR) {
console.log("in");
var data = JSON.parse(responseData['AuthenticateUserResult']);
console.log(data);
},
error: function (responseData, textStatus, errorThrown) {
alert('POST failed.');
}
});