I believe this was addressed in the first few paragraphs of the article: this problem is not about 'information', which is a vague phrase. Rather, it is about how black hole evaporation is fundamentally time irreversible.
Right, but that is using a semi-classical calculation, whereas we know that ultimately any process (evolution of a closed system like the universe) compatible with quantum mechanics needs to be unitary/reversible.
That mismatch is what sets up the BH information “paradox”.
i.e., hawking radiation is itself unconfirmed, so its a "solution" for something that remains unproven :|