You suggest that since its possible to mimic pain, it's impossible to tell if pain is genuine by the signs it leaves, yes?
But that's giving up rather early. Mimicry is imperfect, in that there is no such thing as an entity which is the same in every way as every other entity, except for having to mimic the feeling of suffering. We can look at people with anti social personality disorder, and notice that, while they do feel pain, lack any feeling of grief, shame or regret. And yet they do mimic the feelings well, other traits betray them, such as impulsiveness, frustration and boredom.
You say a parrot can be trained to say "That makes me sad", but parrots will also have a physiological signs of suffering.
Suffering, not pain.
In the recent discussions here about the value of animals several people have argued that what matters is "sentience", or the ability to feel. This goes back to at least Bentham with "The question is not, Can they reason? nor, Can they talk? but, Can they suffer?"
Is "can they feel pain" or "can they feel pleasure" really the right question, though? Let's say we research the biological correlates of pleasure until we understand how to make a compact and efficient network of neurons that constantly experiences maximum pleasure. Because we've thrown out nearly everything else a brain does, this has the potential for orders of magnitude more sentience per gram of neurons than anything currently existing. A group of altruists intend to create a "happy neuron farm" of these: is this valuable? How valuable?
(Or say a supervillian is creating a "sad neuron farm". How important is it that we stop them? Does it matter at all?)