Not in the States. Our notaries glance at your ID before they countersign a document.

This is one of the other jobs of a notary: not vouching for identity, but rather signing off on a document stating that a collection of associated objects are what is described in the document.

Such a document has the same sort of purpose as a certificate of authenticity you'd get from an appraiser; but you use a notary in cases where the thing doesn't need authentication to be valuable, instead being a liquid asset with a clear market value. The notary doesn't write down such a value, or even know it; they just sign off on a description of the item, knowing that the value can later be readily determined from the description by any interested party.

Of course, to make this work, you need the notary to sign off on the contents of the collection right before you secure the collection into storage. Otherwise, you could just make arbitrary alterations to the contents yourself. For this reason—and because notaries don't usually like getting dragged all around town to vouch for things—usually a bank will retain the services of notary of their own, and offer it to safe-deposit-box users as an option. If a notary is used to vouch for the contents on first deposit, then a notary must be used on all further deposits/withdrawals to "retain the chain of custody." This turns the safe deposit box into a managed safe-deposit service.

I don't know of any US bank that uses a notary in quite this way. It's not a notarial act under the model notary act.

A notary can acknowledge the depositor's claim and identity, but can't be held liable for the depositor's claims.

A notary can verify that a man with John Doe's legal ID claims to be depositing one (1) Shroud of Turin and twelve (12) Pieces of Eight from a Spanish Galleon with certificate of authenticity from the Franklin Mint, but the notary is not verifying the truth about or value of the actual contents.

> notary of their own

I have never heard that such a thing as private notary exists.

Right, I didn't mean to imply there is such a thing (and such a thing would be thoroughly useless.) I meant that they have a notary on retainer, that that notary gets almost all their work from the bank's clientele, and that they tend to operate either out of—or right across the street from—the bank itself. They're still an independent notary; but instead of paying them yourself, you pay the bank and the bank pays them to come in and help you. But it's still a relationship between you and the notary, not between the bank and the notary. The bank is essentially serving as lead-gen for the notary.

Anyway, private notaries are a real thing in UAE.

See: http://www.adllaw.ae/private_notary.htm