I can see it being both a roll or fixed DC, depending on circumstances. If a player told me that he was hiding the gem inside the pillowcase on the bed, I'd assign a DC to that. However, no matter how good I am, I'm not generally going to be able to describe every little thing in a room, or think of all of the hiding spots, and neither will the player. However, the 7th level rogue he's playing will likely know ways and places to hide things that neither of us do. I can see the player of the rogue saying, "I hide the gem in the best spot I can find.", and then rolling a stealth(wis) check to see how good a spot was found. Then that roll would be the opposed check for searches.
This.
Even in the case of the pillowcase, I'd probably go for a roll to see just how well it worked. My 4 year old nephew might stuff it in there on top of the pillow with a nice, gem-shaped outline showing. I know enough to stuff it under the actual pillow. An accomplished Rogue might know a trick or two I don't -- including something like it being just as easy but more effective to jam it between the mattress and box spring.
I heard something on a podcast, the other day, that I think applies here (paraphrasing): "Most disconnects people have with skill systems is because they're trying to narrate the outcome before they roll the dice."
In this context, that means that the player should say "I hide the gem in the bedroom," roll the dice, then (maybe) declare exactly where in the bedroom they hid it. The player might be
awesome at hiding things. If the character
sucks, though, it doesn't matter how good the player's idea was. The character may not have thought of that location. They may have thought of it and executed it poorly. They may have thought of it but decided (wrongly) decided that something else was a good idea.
So, four PCs say, "I hide the gem in the bed."
- The Rogue with deft hands and a light touch rolls a 25, total. He runs his hand along the edge of the mattress and finds a seam loose enough to fit the gem through and tuck it into the bedding.
- The Sorcerer with a criminal background, but whose hands aren't quite as deft, rolls a 15, shoving the gem into the pocket created by tucking in the sheet at the foot of the bed and hidden by the comforter. Should be good until someone rubs against the bed or the maid comes.
- The agile, but honorable Monk rolls a 10, and slips the gem into the pillowcase. It's hidden from casual inspection, but any real search is going to find it quickly.
- The War Cleric is smart enough to know the Rogue has a good idea, but rolls a 2. His gauntlet gets stuck in the bedding and he's just pulling it out as the enemy shows up (or, leaves an obvious disturbance for the later search).
Is it mandatory that you roll to hide something? Not at all. I remember the fun in AD&D of searching for traps by describing what the characters are doing, rather than just rolling. That's challenging the players and getting them involved. It's a totally valid style of play. Even today, I really hate the "I search the room" style of play where the fact that the vase is covered in contact poison doesn't matter (3E RAW). I'd prefer to have enough information about the scenario that it matters whether the players are paranoid about touching things, potentially exposing themselves to glyphs, etc.
But.... I also like it when a naive player is able to play a cunning/deft character. Conversely, I don't what the clever player with a Barbarian be able to offset dumped skills with his own abilities. Skills represent what the character is capable of. Some are just better at hiding stuff than others.
Also, live by the sword, die by the sword. If you want to fiat the DC for searching, go for it. As a player, though, don't complain when your sadistic DM uses his own creativity to set a crazy high DC for finding the gem the troll you were chasing hid. If your first reaction is "Trolls are stupid, so it shouldn't be able to hide stuff well," I don't disagree. Some PCs are stupid, too.
Even if you do decide to use a skill check, it's not always narratively interesting. You don't have to roll for everything. If it would be boring/uninteresting/whatever to play out the results of the goblin finding (or missing) the hidden gem, don't do it. Just decide, as a GM. That's why we play a game with a GM.