They would assume that today's utensil is older than the one from 1000 years ago, on the basis of handiwork.
So is the part about the carbon dating of nearby organic material true?
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.
Imagine someone comparing it with a utensil being ordinarily used today having no artwork, with both items being made of the same material.
There might not be a clear answer but that's ok. First of all, carbon dating is a highly inexact science to begin with.
If you submit identical samples to different labs you will get widely differing results.
This question has had a fairly large number of views, showing that there is interest.Usually stone carvings are dated either on the basis of style or on the archaeological context they are found in.