If you find a game that wants to install the XNA Framework, save yourself some time and cancel the installation, as it will not install correctly.
Download the redistributable XNA Framework installer and install it via CXG. Then proceed to install your game.
I've found this behaviour in at least two games: Blueberry Garden and Chime.
Creating a C4P for this and marking it as a requisite for other games' C4Ps might fix this problem. I'll try to explore this.
Edit: Updated link; had XNA 3.1 when this C4 is for XNA 3.0. Also, it seems that it now installs just fine in CXG 10.0.0.