The article says which agency it was (CPB), and quotes the CPB as saying that the agents identified themselves as CPB agents.
It also says that they weren't individually identifiable, which is an issue, but a different issue.
I don't see the CPB supposedly identifying their agency as alleviating the first issue your parent mentioned: habeas corpus. The litmus test is: can a family/friend/attorney reasonably find the arrested/detained person within a few hours?
