Further down in the article it explains that the case was regarding a husband's right to notification. I agree the case study one phrase is misleading and has nothing to do with PPH vs. Casey.
But strictly in the part about Alito and husband notification, the writer correctly states that the case was merely about notification.
It's interesting that our discussion is a microcosm of the Alito/PA case, i.e., broad vs. narrow interpretation.