Original: I would agree with you that the correction to "comprised of" is the better of the two options, but not for the reason you give.
If the sentence reads "A committee comprising eminent members...," then that means the committee makes up the members. That is illogical because the members are (each) singular people, while the committee is a collective.
What makes more sense is "A committee comprised of eminent members..." In that case, the singular members collectively make up the committee.
In either case, the sentence is still in passive voice because "was set up" is the main verb phrase, and it's passive. Everything from "A committee" to "institutions" is just one big noun phrase.
Edit: Interestingly, Merriam-Webster lists both opposite interpretations as possible meanings of comprise: the first meaning where parts comprise the whole, and the second meaning where the whole comprises the parts.
There is a nice editor's note about how the interpretation of the whole comprising the parts was most common for a long time but now, more recently, the parts comprising the whole (the version I say that I think is more correct above) has become more common.
All that said, I think it's fair to say both "A committee comprising..." and "A committee comprised of..." would be perfectly grammatical. Your textbook appears to favor the more traditional meaning, whereas I, apparently, have come to regard the newer meaning as more correct.
Both versions are completely intelligible either way – I would interpret the sentence the same way no matter which revision you made – but the one I argue for in the top half of this answer is the one that sounds more natural to my ear, as a native speaker of American English. Others may well disagree.