This is quite a curious situation to me, Taka, and I think you have a good case for confusion.
I immediately thought 'they' referred to 'answers'. But on closer inspection of the logic, I thought this:
According to the quoted sentence--
The essence of scientific research is discovery. A genuine scientific problem is one where the answer is unknown. If the answer is prescribed (given), it is considered known. What doesn't seem to come into play here is whether that answer is true or false. (That would be the function of 'scientific proof', not scientific research'.) What's not genuine, when the answer is prescribed is the scientific problem devised to discover that answer. Ths scientific problem cannot be a genuine one if the answer to it is already known.
So I now say, 'they' refers to 'scientific problems'.
If I were proofreading the quoted statement, I believe I'd have to comment on 'they' as having an indefinite antecedent.
What will other readers say?