Yes, they do indeed although birds are still considered to be theropods so it would only make sense to share a common theropod ancestor. All birds - flight capable and flightless - can trace their genetic ancestry back to the Late Jurassic Period of the Mesozoic Era. read more
In theropods and prosauropods, the only way for the palm to face the ground would have been by lateral splaying of the entire forelimb, as in a bird raising its wing. In carnosaurs like Acrocanthosaurus, the hand itself retained a relatively high degree of flexibility, with mobile fingers. read more