The standard of care to determine documents are accurate varies.
For example, in an ordinary notarized document, notarizing the signature of an imposter will ordinarily only impose liability on the notary for harm caused by the fraudulent imposter signing, if the notary is negligent, i.e. fails to use the reasonable care of a similarly situated notary.
But, suppose that instead of a notary, the imposter uses a fake ID to get a bank to confirm his identity as part of a "guaranteed signature", which is a parallel system of confirming people's identities arising from an industry organization and mostly used to confirm identity in life insurance payouts and other non-probate transfers (e.g. pay on death bank accounts). In the bank that guarantees the signature is duped, the bank has strict liability without regard to fault to the party that is harmed by the imposter's bad signature.
In the case of fake signatures on checks, there is an elaborate web of statutes in Articles 3 and 4 of the Uniform Commercial Code and some related federal regulations, but basically, it boils down to the harm from a forged check falling on the person who dealt most closely with the imposter.
The standard for a Fake IDs used to get alcohol is particularly tricky because rather than flowing from a common law rule, it usually depends upon the exact language of a liquor regulation statute and related regulations, so it is often non-uniform.
There is not a general rule governing this situation and that situation is very common in American law. More often than not, you can not determine the correct answer to a legal question by simply applying a general rule to a new situation. Law is not physics.