I think what's interesting about attributing such crucial importance to "empirical adequacy" (meaning that no physics theory should ever try to predict more than we could ever possibly observe, and any that do are by definition being equipped with extraneous features that are of no value and should therefore be removed) is that, although GR seems to allow a distinction between "infinite" and "having no boundary", no such distinction should ever exist in any theory of cosmology. This follows from the fact that we already know that any distinction that is made between our universe being infinite and having no boundary would have to be a distinction that exists entirely beyond the observable horizon, hence does not respect this principle of empirical adequacy that the above article attributes such crucial importance to. Put differently, the principle says that the "cosmological principle" that the universe is homogenous on the largest scales can only ever be applied to the observable universe, and there would never be any valid purpose in extending it beyond the observable horizon.
This makes perfect sense, who cares about the difference between a universe that is homogeneous out to the observable horizon, and then does something completely different beyond that horizon, versus one that continues to be homogeneous everywhere. That would be a classic example of angels on a pin, something physics cannot falsify. Therefore, it follows that the distinction between "infinite" and "having no boundary" in our universe can forever be put to bed as an entirely moot, and therefore physically meaningless, distinction, and that particular chapter can be set aside as having no further physical importance.
But one potential weakness in this principle of "empirical adequacy" is it sounds a lot like a principle of "denial of the importance of hypotheticals." That makes sense if one thinks physics should work like saying "given that the universe is the way it is and obeys the laws it does, what is the probability distribution for some given observation." But others think that physics can also include questions like "what is the probability distribution for the universe to be the way it is." In that case, one needs hypotheticals that go beyond empirical adequacy, i.e., one includes in one's models hypotheticals that could never actually be observed (a la multiverse thinking). Whether or not multiverse thinking counts as valid physics is an important question, and I think it challenges the concept of empirical adequacy.