No, that would be a bad DM call. The DC is 20. He succeeded. He found food. End of story. Why would he not find food after I set the DC and he succeeded? Why are you taking a success away from the player?
Exactly... tho should note the same can occur if the Gm withheld the Dc and the forager rolls 20 or above and when told nothing acquired he is surprised as well. (In my games, that "the 23 did not get you any game or water" would be narrated with descriptions of what the character saw like tainted pools, dried pools, poisoned carcases or maybe just a whole lot of stone animal statues not too far out from camp.) In other words the unusual result the unexpected result would be and should be seen as a "clue".
So, thats why i am not gonna dump on the player who says "i search for stuff over there" or "i search the room", gets a DC assigned openly or kept private, gets a high result and is surprised at a high result is resulting in nothing - because its exactly what would happen if the other character was outside and said " i go looking for food and water" and the same outcome occurred.
Thats why i use "wandering treasure" in my games. i see the "GM pre-determined key in drawer" type of example as the equivalent of set-piece outdoor encounters, not the *MINIMUM REQUIREMENT* for success of searches in general.
So again, to me, not as clear a "bad player" case as it may be to some.