Birds are members of a group, saurischia, best known for having "reptile-like" hips. Even though not all members of the group have that characteristic, that doesn't affect the validity of the group. In cladistics, which is by the far the dominant approach to taxonomy nowadays, taxons should be monophyletic groups or "clades" comprising a common ancestor and all its descendants.

There is current debate and research as to whether the traditional saurischia is a monophyletic group or not, and some classifications put ornithiscians as closely related to theropods with saurischia either redefined without theropods included or not used at all. But bird anatomy does not by itself invalidate the traditional view.

https://en.wikipedia.org/wiki/Saurischia

The anatomy was named before they understood the evolutionary relationships between living reptiles and birds and extinct non-avian dinosaur lineages. There were dinosaurs unrelated to those which evolved into birds which had hip anatomy which looked similar to the hips of modern, living birds, so they described them as the group with 'bird-like hips,' not knowing how confusing a hundred more years of paleontology research would cause the name to become.

So, birds have bird hips, not lizard hips, in a purely descriptive sense that ignores established terminology, but these 'bird hips' are not hips of the type that put them in that named and defined group of extinct dinosaurs. Those modern bird-like bird hips happen to be descended from the hips of dinosaurs which had hips that didn't look as much like modern birds' hips at the same time as there were dinosaurs which, coincidentally, happened to have hips grossly like modern birds', despite not being direct ancestors of birds.

Coincidence, lack of current knowledge when anatomy was named, and the classic problem of taking descriptive morphological terms to imply origins, which is really the terminology's fault. Is this hip business really any more confusing than that we use the 'saur' affix which means 'lizard,' literally, for non-lizard species? Lizards are a specific thing, and dinosaurs (pardon the term) aren't lizards....but nobody's complaining about that term, are they? Because they were named when nobody knew any better, and we all acknowledge and agree that the name means they're like lizards, but real big and scary-like, to keep the term useful, not forget the literal etymology, and finally not ignore the newer science.

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The separation of dinosaurs into two groups (saurischia and ornithischia) occurred long before the modern idea of birds being considered dinosaurs was contemplated. Current evidence suggests birds are descendants of a subset of therapods, which were saurischia. Obviously their characteristics changed over hundreds of millions of years of evolution.

Basically they aren’t saurischian because THEY have lizard like hips but because their distant ancestors did.

The fact they are so different from their ancestors is why I, frankly, think calling them dinosaurs is grossly misleading, and scientific pedantry. It leads to exactly the kind of confusion you are experiencing.