Don't know how that extension works, but it's breaking CBs anti-spoof protection. As we're not the developer of ComponentsAnywhere I've no idea how they're outputting components to cause such an issue but in theory should work fine calling normal Joomla API for rendering a component. Can't really help with such issues though unless your normal CB registration form also has same issue.
The problem comes definitly by the plug components anywhere. My Problem is now i need the registration form around other content like the demosite you shown above my trhead.
Our demo site is just using normal module positions as part of the template. You shouldn't need to use something like ComponentsAnywhere for that. Most templates come with quite a few module positions or they offer features for changing the layout so you can have module positions anywhere you like.