https://carrier.biology.utah.edu/Dave's%20PDF/theropodturning.pdf
Scroll down to "Running posture that reduces rotational inertia" (Second last page). Note that the author isn't saying the horizontal posture is wrong. It's just that they may have switched back and forth depending on the situation.
While I won't go ahead and make any concrete statements or tell anybody to take this study as gospel, to me it does make a lot of sense. Aside from what they say about rotational inertia (which might provide an explanation for what theropod arms for used for. You can see a similar thing with bipedal lizards today), this is the only thing I've come across that explains the "theropod posture" found in fossils. Almost every single theropod fossil has the exact same posture. While the tail and the arching of the neck may be explained by water transport (they did this with chicken skeletons to explain the death pose), that still didn't provide a convincing enough explanation for why the legs almost always looked swept back. I took an image of black beauty and then rotated it 45 degrees, and it's almost a 1:1 match with the bottom image.
You don't really see this with fossils of herbivores. Look up duelling dinosaurs. The juvenile trike basic anatomy looks right, whereas the nanotyrannus, if viewed from a horizontal perspective, looks like it's "float crawling." Same with the camarasaurus fossil. While the legs are slightly tucked in a backward pointing direction (because obviously very few living things will have a completely natural posture when dead), it's not as drastic as it is with theropods.
(the arched tail can probably be explained by water transport)