They don't have to use ajax. They can load an image with an arbitrary url and pass the keypress data in the url parameters, or dynamically create a script tag, or create an iframe and submit a form in it, etc. The script tag method also lets them get data back from the remote endpoint, if the remote endpoint is kind enough to encode it as JSONP.

I think he's referring to a hostile script trying to bind to keydown -- usually you shove the banners in iframes to limit this possibility when you include external untrusted content. I assume the same holds true here, though.

The Same Origin Policy can be overridden by the site accepting the connection (http://www.w3.org/TR/cors/), so assuming that site is hosted by the attacker it wouldn't be helpful. If the site used (and the browser supported) a Content Security Policy (http://www.w3.org/TR/CSP/) you could restrict such outgoing connections.