A formula with no traceable source is not the same thing as a false one, and the distinction is the whole point of flagging it.
There is no evidence that anyone fabricated this verse with intent to deceive. The likeliest history is ordinary and blameless: a teacher composed or adapted a benediction in correct Sanskrit, students assumed anything in Sanskrit chanted at the end of a class must be ancient, and the assumption hardened into a citation as it was repeated. That process has produced a great deal of what circulates as traditional material, in every tradition, and it usually leaves no fingerprints.
What makes it worth stating is the asymmetry in how the claim is used. Presented as a modern benediction, it is what it is. Presented as Vedic, it borrows authority it has not earned, and that borrowed authority is doing commercial work in a large industry. A studio that tells students they are reciting words three thousand years old is making a factual claim to people who have no way to check it.
Compare the cases in this collection where the ancient attribution does hold and can be pointed at: a verse with a book, hymn and stanza number in a printed critical edition, or a formula quoted in a canon with a chapter reference. The difference between those and this one is not a matter of degree.
The editorial position taken here is that a widely used item with an unverified provenance should be included and flagged rather than excluded, because excluding it would leave a reader with no way of finding out.