The item's time period of origin can be narrowed down by substances found in adjacent sediment deposits and carbon dating of these substances left in the deposits on the object itself.
Radiocarbon dating is one of the most widely used scientific dating methods in archaeology and environmental science.
In fact, a lot of labs not only require you to estimate the age of the sample, they require you to your estimate. A scientific measurement is "blind", meaning the tester does not what the result should be ahead of time; carbon dating does not fall into this category.
As far as stratigraphy is concerned, infiltrated remains, the kind of error you describe are always a concern.
This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.
As explained below, the radiocarbon date tells us when the organism was alive (not when the material was used).
But the items were actually much older than even the curator. Inspecting the handiwork on the sculpture itself is subjective to assumptions about possession of skills at different time periods. Take present day example : Utensils from 1000 years ago in a museum can have exquisite artwork, embellishment, detailing.
Once an organism dies the carbon is no longer replaced.The only organic material they find is the remains of the curator.They date it, and from that, peg all the stone sculptures found in the museum at 2000 years old.The problem with this approach: Suppose a museum in present day has several stone monuments from varying dates.And they're cleaned and maintained quite well by the curator; there is no organic material on them.So, one excavated stone might look brand new, and another one very ancient and degraded.Usually stone carvings are dated either on the basis of style or on the archaeological context they are found in.One day the whole museum is suddenly buried under enormous amounts of inorganic material, with the curator trapped in and crushed to death.2000 years later a team of archaeologists uncover this place.Usually any kind of single piece of evidence is not sufficient to date an object; an overwhelming and diversified set of evidence is necessary.For example, if a bone is found in a tomb, that is not enough to date the construction of the tomb, because the bone could have been placed in the tomb long after it was constructed.