So no, the title is not really wrong unless there is a yet undiscovered bird that's even larger. The elephant bird was the biggest bird (or avian-dinosaur) that ever existed. It was smaller than other non-avian dinosaurs but these were not birds so no point comparing.
The confusion you are making is sometimes described as politician's syllogism. [0]
1) All birds are dinosaurs
2) All land dinosaurs are dinosaurs
3) Therefore, land dinosaurs are birds