On the StumbleUpon extension page, they state:
Chrome does not allow DOM injection into some pages so the toolbar is not visible on those pages (including chrome product URLs like the extensions page, and newly opened tabs)
This is in agreement with Chrome's developer documents. From the Extension Developer FAQ:
Can I add a content script to
No. The extensions APIs have been designed to minimize backwards compatibility issues that can arise when new versions of the browser are pushed. Allowing content scripts on
The reason that replacing the content hosted at these URLs entirely is allowed is because it forces an extension developer to implement all of the functionality they want without depending on the browser's internal implementation to stay the same.
Basically, with Chrome's current Extensions API, the only way StumbleUpon would be able to put their bar on to the new tab page would be to completely override the current tab page, which would mean they would have to write their own. This would also mean it would be up to StumbleUpon to make sure that newly installed apps and extensions showed up on the page, etc., which is a lot more work than they probably want to take on.