Yes, I think this is a correct assessment of the Buddha’s position.
I think that ‘dukkha’, in this particular sense, is primarily a negation. So the value system is something like this:
If X is not a permanent, unconditioned source of happiness, then it is not sukha.
Whatever is not sukha is deemed dukkha.
A similar statement is when the Buddha says “Whatever is impermanent is dukkha.” If we go by this agreed upon definition, then he’s simply stating a basic value system: if it isn’t permanent, it isn’t fully adequate. Therefore, it is deemed “inadequate.”
Here, “good” or “adequate” basically meaning “supreme, perfect, permanent happiness.”
Painful feeling of any kind is automatically excluded, because it isn’t even happiness, let alone perfect happiness.
Impermanent or changing things are excluded, because they are not perfect or permanent happiness.
Conditioned or dependent things are excluded, because they are not permanent or independent happiness.
In this way, we can see how a mere system of values places conditioned experienced in the category of ‘dukkha.’