Targeting a creature does not free them from a cursed item.
You are on the right path with your logic, there is indeed a separate interaction between removing a curse from a player, and from an item.
Most curses in the game are single-instance effects that inflict the curse.
The most common example is the bestow curse spell, which inflicts a curse for a duration when the target fails its saving throw. Targeting a creature with the remove curse spell or by using the Panacea effect of a transmuter's stone, would clear this curse permanently, as the source of the curse has already resolved (the bestow curse spell).
Cursed items break this mold, by being a persistent source of the curse.
As you already referenced, remove curse has specific verbiage regarding targeting cursed items, which does not remove the curse, but does break attunement. By referencing the "Curse" section of a cursed item, you can see that the curse is extended to any creature that is attuned to the item. So what happens when you cast remove curse on the attuned creature instead?
- Remove curse is cast, targeting the creature.
- Remove curse resolves, and ends the curse.
- The item is still attuned, so the curse instantaneously re-applies to the attuned creature.
This interaction can be inferred simply by the fact that remove curse cites specific conditions for dealing with cursed items. Since this specific ruling is assumed to overrule the general rule regarding curses, it maintains that using remove curse or Panacea on the creature would have no lasting effect in this situation. Panacea in particular gives no mention of effects on items, so it cannot be assumed to override the specific ruling set forth by cursed items (in that they curse their player as long as attunement is maintained).
Also of noteworthy mention is this question which gives an example of the Sword of Vengeance, an item that has specific rules regarding another way in which to remove a curse. This reinforces the assumption that removing non-standard curses requires a specific ruling stating how to do so.