That’s something I often wonder about when it comes to site or non-organic artifact dating.
The organic remains may be no more related to when and who built the thing than any trash I leave at Stonehenge is.
If you dug a pit at Stonehenge, burned your trash in the pit, and then recovered the hole without leaving any sign of the hole, sure. But you're not doing that, nor is it likely that you could pull it off. Past disturbances of the ground or stratified deposits are visible, as the filled-in ancient robber's hole leading to the door of Tut's tomb was visible to Howard Carter.