A third party (CDN provider) can easily track visits entirely server-side across all of the sites that it serves. Typically this is sites owned by lots of different companies users could otherwise visit without any of those companies knowing of visits to any other companies' sites -- the CDN knows.
This also comes up when the CDN handles SSL termination.
I wouldn't want my page behind a CDN. CDNs make users much more trackable across sites.
My point isn't that CDNs are bad for everyone. My point is, once more, that most questions are not as simple as they may appear.