The latter. Items can show up at any depth, but if the depth is less than their native depth, then the item has to pass an "out of depth" check first, which gets harder the more out of depth you are.
I think there's a limitation that prevents artifacts from showing up in town, so e.g. Farmer Maggot won't drop them, but he could theoretically drop a Ring of Speed and I've gotten dungeon spellbooks from him in the past.
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