You can make it even more obvious. The food is hot on the table and a candle is burning when there's a sudden emergency, everyone leaves and doesn't return for an hour during which the table and the food and the candle are completely unobserved. When everyone returns the food is cold and the candle has burned down a couple inches.
So if the table and food and the candle go out of existence while unobserved, what causes them to return to existence in such a way as to perfectly match the passage of an hour of time? In other words, it isn't enough just to store the state of the table somewhere while it is non-existent. You must also store the effects of the passage of time.
The example actually needs a little improvement because the unobserved room is still connected to the rest of the universe. Some of the heat from the food and the candle will escape the room where they can be observed, and of course there are innumerable other connections with everything else. Isolation from all observation is required for this to be the example Eliyahu intended it to be, but even if that were the case there's still all the things you mentioned.
--Percy
Edited by Percy, : Add a little more detail at the end.