Maybe T. Rex did lumber around like an elephant because of his size, and not like in the movies, but a lot the other dinosaurs were as big or even bigger, which according to this logic would have made them even slower.
It reminds me of the old joke (really old) of two hunters being chased by a bear. The first hunter turns to the other hunter and says I don't think we can out run the bear. The second hunter says to the first, I don't have to run faster than the bear, I just have to run faster than you.