I heard about this account as well, and it would make the most sense, but did the tent exist in his day? They had the Temple but I always wondered if the tent was still in existence when Jerusalem was destroyed by the Babylonians.
I forget where I read it (probably in extra-biblical rabbinic writings) but I think it was generally thought that after Solomons temple was completed, the desert tabernacle was disassembled and stored in the temple complex, perhaps even inside the Holy of Holies.