That fails the smell test. There aren't many four-legged things that are slower than the two-legged thing. How would being slower be an advantage in crossing open spaces? It not only takes you longer to get to the food, it makes you an easy mark for the things that want to turn you into food.
My hunch is that the "tool thing" came first, and bipedalism arose because there was a higher valued use for hands.
Your "hunch" is the most widely accepted notion today. Traditionally, it was believed that bipedalism was the result of a larger brain-to-body size---that walking upright was a singularly human trait because humans had the largest brains. The fossil record changed that thinking. Early forms, including Australopithecus were totally bipedal yet, possessed a cranial capacity not much larger than the chimpanzee.