That's a BS excuse on the center's part. That doesn't exclude or overlook the fact that Evangeline wasn't notified prior. It hadn't even been a week or enough time to properly evaluate Jules, so there's no way the security was that lax that they just wouldn't be able to account for someone who is, again, the sister of a police detective. Either way you slice it, either the center has terrible security or terrible communication for not even thinking of letting Jules's only nearby relative know that she'd vanished.
It also still doesn't explain how the coast guard found Jules so quickly. Everyone keeps talking about how it's Christmas Eve, so resources are thin. So either she didn't sink very far, or they just miraculously found someone they couldn't easily identify, but managed to anyway? It's not like the coast guard would've known that Jules was in a treatment center, so they'd have no reason to contact them.