Yes, black hole information paradoxes can exist given current theories of how black holes work, because we simply do not have enough information as to how black holes work. It is an interesting theory, and one that contradicts other things that we know about physics. It is possible that the information paradox exists, despite other principles of physics. We will have to study it more.
Black hold information paradoxes can exist given the current theories of how black holes work. This is because we only have theories on how black holes work, and no concrete evidence. This means that almost any other theory out there can exist as there is no solid information on them.
If you conceptualize two things, one, that the universe is growing, and two, that our knowledge of the universe is growing, then you can find out that we can be a bit more dynamic and open minded about previous conceptions of the universe. A black hole as we know it could change.
The black hole information paradoxes can exist in spite of our current theories of how black holes work. In reality, we don't know every property of the black hole, and such theories are only educated guesses backed up by evidence. They aren't necessarily scientific truths and allow for paradoxes and other unexplained issues.
The idea of a paradox specifically indicates that several things can't be reconciled, which I don't believe can really exist in science. Its true that there are many paradoxes, but these are more questions pointing out holes in our reasoning and knowledge, rather than a factual and real lack of reconciliation.