First, yes, It's all just theoretical discussion until there's case law. Something like this, that's pretty unlikely to happen. This is a discussion on a Internet forum, one would think discussions are just that. I don't see the need to get belligerent about it.
As I said, beyond the explicit perjury penalty, there would certainly be (in theory) penalties for falsifying information in the notification.
Personally, don't think they'd actually be criminal beyond (vi)'s explicit perjury penalty (if it applied in anyway), but was just relating the opinions of my law professors I've had the discussion with.
The main argument (ignoring any that address the grammar of the law, which very fit and miss when talking American English) is that (vi) mentions the accuracy of the information in the notification. In addition to (v) that address the good faith belief (and (v)'s mention of agency). The overlap suggests that the first clause in (vi) has to be operative in some manner for it to be included.
If you want to talk plain text (which really means little given the looseness of grammar in the law, even major SCOTUS decisions have ignored sentence clauses of the Constitution for seemingly arbitrary reasons), In (vi), neither the second or third clauses can be individually excluded with the sentence making sense. The perjury clause is subordinate to the accuracy clause, but is adjunct to the agency clause.
There's no way to parse that sentence's grammar that really makes sense, Whether you want the perjury to apply to just the agency, just the accuracy, or both. So I don't think an appeal to the 'plain text' of it clears anything up.
I doubt there's much of anything useful in terms notes on legislative intent for something that minute, but can't access that easily from off-campus anyway, and given the politeness of the discussion, I doubt it would matter.
Again, just opinion and the results of my reading and discussion with my law professors. Take it for what you want. There's no need to get rude about it.