From a practical point of view, the baby universe theory is no different than the “information is lost” theory. Although it might be satisfying to think that information is not “really lost”, there is no way in which we -- in our universe -- would be able to tell the difference. The distinction is philosophical, not physical.

There is a different theory not mentioned prominently on that page that in my opinion provides the most useful resolution: Black Hole Complementarity. In a sense it is not a satisfying resolution, because it basically states “the paradox is not a paradox”. It is very counter-intuitive, but that is a problem with intuition. The wave-particle duality of light, which is nowadays not really considered a paradox any more although it was ~110 years ago, is a good analogy. As always happens with questions like these, in the end the answer is “that is a nonsensical question to ask”.