I don't believe it's a confusion over the fact, but perhaps the wording of the comments? This was the clearest statement of it I've seen. And, as far as I know, you are correct.

But I'd point out that there are qualifications that a church (broadest sense) has to go through before it can appoint representatives to be in a position to sign those documents. They can't just be anyone off the street self-proclaiming they're qualified. The standards are not high - filing some papers - but neither are the requirements for becoming a county clerk's deputy who can do the same thing (filing some papers).