Don't worry, I set him straight on this matter.
I'd like to know what 'straight' functions as. Does it function as being an adverb, or an adjective?
I don't know which is well fit to interpret the sentence correctly, because both seem to be fine for me to adjust to the sentence, regardless of whether it is an adverb or an adjective.
However thinking about the sentence, there seems not much difference in meaning whether it is used adverbly or adjectively.
A similar problem goes by 'right'
They never get the facts right
In this case as well, regardless of how it is used, both seem to be interpreted perfectly.
However, on the whole, I think they might be used adjectively to complement the objects.