Your point is fair; you're entirely correct, but allow me to clarify mine. The existing CSP configuration on the 'unsuspecting' server will do one of two things:

[a] allow the cross-origin request to be made, in which case the malicious website could've just made the actual request instead and obtain the body of the actual response without any of this BEAST/CRIME trickery

[b] deny the cross-origin request, in which case there is no reflected data in the response, preventing the malicious website from performing the reflected data or data-comparison attack demonstrated in the paper

(If I'm wrong, what am I missing?)