Mind you, I say knowingly false. Big companies unknowingly make false claims all the time, because they don't know what-all they actually own — but you can't sue them for that anyway, since there's no mens rea there.

No, that's not what I meant. I meant, "any claim that can be interpreted in a court of law as being equivalent to saying you intend to sue for copyright infringement and have a legal basis to do so."

In the same sense that a handshake contract is still a binding contract, a regular letter telling someone that you're aware they're violating your copyright — and which doesn't explicitly disclaim any interest in pursuing legal action — can still be interpreted as a threat of legal action; and therefore, if proven to be based on knowingly false claims, as injurious perjury.

To be clear, it's not YouTube making this claim; it's the IP owner making the claim, when they register the IP in the ContentID system. Such a registration is equivalent in the spirit of the law to notoriously claiming 1. you are the IP's true owner, and 2. that you do not license use of your IP for use by others without your prior consent; and that therefore 3. you have an interest in pursuing action against all future unlicensed use of your IP, whether that action is using the DMCA, within the framework of the legal system outside of the DMCA specifically, or through extralegal means.

By analogy, consider what sort of verbal claim of intent to commit a crime (e.g. selling illegal drugs) is necessary in a police sting to trigger an arrest. You don't need to actually have committed the crime (i.e. hand the undercover officer any drugs, or even prove you have any drugs); you merely need to make it clear that you are actively working to set up the conditions necessary to carry out the crime (i.e. to agree/negotiate a price for the drugs you may have.)

In this case, a judge would basically be looking for the point of "stated intent to commit perjury." Which happens as soon as the ContentID for the video is registered!