@Stabbey, you are correct that it is only mentioned in the DMG
Originally Posted by DMG pg 139
Most methods of identifying cursed items, including the identify spell, fail to reveal such a curse...A curse should be a surprise to the item's user when the curse's effects are revealed
I agree that the Identify spell should contain said caveat.
Originally Posted by Stabbey
As an aside, under your interpretation where Identify does not reveal curses, how is one supposed to know if an item is cursed without attuning to it and becoming cursed?
That's exactly the point, that players don't realize its cursed until they've attuned to it. And at that point, they become cursed and cannot remove the item!

Why bother making cursed items if players, upon finding them, can easily notice the curse and thus won't attune to the item?