While likening a kid forging his signature to a proficient forger doing a fake doc is sketchy, even as a kid I did the signature several times, especially if I had something to go by. If we had other folks in on it they would look at it too.
At a professional level most folks review their work and while it's not always perfect or their best work, often the really bad mistakes are caught by either their own review or other review before release.
And yes, PCs font "know the roll" but they should be able to 9bserve the products and make assessment.
Let me ask this another way...
A battle master is in combat with a foe. The battlemaster rolls a natural 19 and missed (narrated however you do that thing.)
If that player then decided "oh crap, this is not gonna work. I need ax20" and changes tactics - is that forbidden or considered inappropriate at your table? Do you tell that player "The PC is not aware of the roll."
If that same player rolled a natural 2, treats it like " just a bad effort" and keeps swinging, do you tell them "The PC is not aware of the roll."
Obviously, whether or not the forgery us good enough to get past a given guard or inspector is uncertain, but to me it seems that whether or not its even close to a decent forgery would be known to a proficient forger, even if not a kid skipping school.