I've separated them purposefully because I think there's an important semantic distinction. The boredom you describe is driven by disinterest due to neurochemical dysfunction.

That's distinct from boredom as a state of mind which assumes or asserts that curiosity, entertainment, etc, are presented and consumed. There is not necessarily a chemical imbalance imposing this state on the mind.

If you like, you could reword the sentiment as; only boring people are bored (and those with depression are not necessarily boring).

I've considered that phrasing previously but found it diminishes the concept.