It’s not false swearing if they believe what they’re swearing to.
They said they got a call, purported to be from the girl, and want a search warrant to check it out. That’s all true.
I supposet there’s a chance this will affect the criminal cases, but I haven’t found anyone that said it would affect the childrens’ status.
If your girl friend has a phobia against polygamy and her supposed experiences, you adopt this view, and search the Internet and find a group that fits your phobia, you file a complaint based on hearsay and your girl friends supposed experiences, is that not false swearing.