I think Kuhn’s answer is that facts cannot be paradigm-independent.
I liked this take on it, from Steven Horst’s Cognitive Pluralism, where he’s quoting some of Kuhn’s later writing (the italics are Horst quoting Kuhn):
A historian reading an out-of-date scientific text characteristically encounters passages that make no sense. That is an experience I have had repeatedly whether my subject is an Aristotle, a Newton, a Volta, a Bohr, or a Planck. It has been standard to ignore such passages or to dismiss them as products of error, ignorance, or superstition, and that response is occasionally appropriate. More often, however, sympathetic contemplation of the troublesome passages suggests a different diagnosis. The apparent textual anomalies are artifacts, products of misreading.
For lack of an alternative, the historian has been understanding words and phrases in the text as he or she would if they had occurred in contemporary discourse. Through much of the text that way of reading proceeds without difficulty; most terms in the historian’s vocabulary are still used as they were by the author of the text. But some sets of interrelated terms are not, and it is [the] failure to isolate those terms and to discover how they were used that has permitted the passages in question to seem anomalous. Apparent anomaly is thus ordinarily evidence of the need for local adjustment of the lexicon, and it often provides clues to the nature of that adjustment as well. An important clue to problems in reading Aristotle’s physics is provided by the discovery that the term translated ‘motion’ in his text refers not simply to change of position but to all changes characterized by two end points. Similar difficulties in reading Planck’s early papers begin to dissolve with the discovery that, for Planck before 1907, ‘the energy element hv’ referred, not to a physically indivisible atom of energy (later to be called ‘the energy quantum’) but to a mental subdivision of the energy continuum, any point on which could be physically occupied.
These examples all turn out to involve more than mere changes in the use of terms, thus illustrating what I had in mind years ago when speaking of the “incommensurability” of successive scientific theories. In its original mathematical use ‘incommensurability’ meant “no common measure,” for example of the hypotenuse and side of an isosceles right triangle. Applied to a pair of theories in the same historical line, the term meant that there was no common language into which both could be fully translated. (Kuhn 1989/2000, 9–10)
While scientific theories employ terms used more generally in ordinary language, and the same term may appear in multiple theories, key theoretical terminology is proprietary to the theory and cannot be understood apart from it. To learn a new theory, one must master the terminology as a whole: “Many of the referring terms of at least scientific languages cannot be acquired or defined one at a time but must instead be learned in clusters” (Kuhn 1983/2000, 211). And as the meanings of the terms and the connections between them differ from theory to theory, a statement from one theory may literally be nonsensical in the framework of another. The Newtonian notions of absolute space and of mass that is independent of velocity, for example, are nonsensical within the context of relativistic mechanics. The different theoretical vocabularies are also tied to different theoretical taxonomies of objects. Ptolemy’s theory classified the sun as a planet, defined as something that orbits the Earth, whereas Copernicus’s theory classified the sun as a star and planets as things that orbit stars, hence making the Earth a planet. Moreover, not only does the classificatory vocabulary of a theory come as an ensemble—with different elements in nonoverlapping contrast classes—but it is also interdefined with the laws of the theory. The tight constitutive interconnections within scientific theories between terms and other terms, and between terms and laws, have the important consequence that any change in terms or laws ramifies to constitute changes in meanings of terms and the law or laws involved with the theory [...]
While Kuhn’s initial interest was in revolutionary changes in theories about what is in a broader sense a single phenomenon (e.g., changes in theories of gravitation, thermodynamics, or astronomy), he later came to realize that similar considerations could be applied to differences in uses of theoretical terms between contemporary subdisciplines in a science (1983/2000, 238). And while he continued to favor a linguistic analogy for talking about conceptual change and incommensurability, he moved from speaking about moving between theories as “translation” to a “bilingualism” that afforded multiple resources for understanding the world—a change that is particularly important when considering differences in terms as used in different subdisciplines.
I liked this take on it, from Steven Horst’s Cognitive Pluralism, where he’s quoting some of Kuhn’s later writing (the italics are Horst quoting Kuhn):