Maybe, but remember that nonconstructive proofs exist, and aren't uncommon in mathematics.
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The proposed models described in the article are not proofs. Physics is not the same as math; you don't prove things in physics. You propose models and test them against data. The models being proposed have not been tested against data, so it's way premature to say they resolve anything. They are interesting proposals which hopefully we'll someday be able to test.
Perhaps, but the information paradox itself is a result of theoretical models, not data.
> the information paradox itself is a result of theoretical models, not data
Yes, agreed.