As an alternatve to flipping the bird over, you could lodge it firmly in the top of a tree for some added stability
Seriously, they can take pictures with the stars in, but they won't give you great results without doing a lot of stacking/combining & correction work in photoshop.
The long exposure times are limited (8sec is the longest I think). The camera is also on a mobile platform (quadcopter) rather than held rock steady on a tripod. Added to that the cameras are also mounted on an electronically controlled gimbal that is always jigging around and is never really static, so there will always be a subtle amount of blur on the stars.