I created a new world with the seed below. In this world, I encountered a dungeon close to the surface with the customary two chests. Once I cleared away the sand and mined the chests, they continued to appear in their spot even though they were in my inventory. I could see them, but they weren't really there – when I attempted to mine them again, I mined the wall behind them. (see images)

This behavior continued until I exited and reentered the world, at which point the phantom chests no longer appeared.

If you want to try this yourself, the seed is 7277340328354678365. the sunken dungeon is between the village and the temple.