From my understanding, that invokes the black hole information paradox. There should be some way in which the information of what went into a black hole is retained, a possible answer being with the Hawking radiation.
We just don't know enough about black holes to say for sure that the insides can not be studied in some manner. That's kind of why a theory of quantum gravity is so relevant, without it, the inaccessibility of the inside of a black hole remains at odds with key components of quantum physics.
Eg The current theory is that black holes release Hawking radiation, and studying that over the lifetime of the black hole might reveal information about the matter that went in. Understanding how this information is encoded could reveal things about the inside. Other possible explanations are that near the point of evaporation, when the black hole shrinks down to a size where quantum effects dominate, the information within becomes accessible, which could again allow potentially studying the inside.
Using information from Hawking Radiation to understand what went in: while it might be possible, isn't this on the same practical level of unscrambling an egg? Sure we could do it with nanobots but is that really a possibility or just a mathematical curiosity?
Given the amount of mass typically involved, probably just a mathematical curiosity, but if that's the only way we can figure out to try to understand the inside, maybe we'll eventually be able to generate microblackholes from tiny amounts of matter, collect the hawking radiation and study those in this manner (they'd evaporate pretty quickly).
Edit: I forgot to add in my original post that there's also just the possibility that the mechanism by which this paradox is resolved still hides the inside.
We just don't know enough about black holes to say for sure that the insides can not be studied in some manner. That's kind of why a theory of quantum gravity is so relevant, without it, the inaccessibility of the inside of a black hole remains at odds with key components of quantum physics.
Eg The current theory is that black holes release Hawking radiation, and studying that over the lifetime of the black hole might reveal information about the matter that went in. Understanding how this information is encoded could reveal things about the inside. Other possible explanations are that near the point of evaporation, when the black hole shrinks down to a size where quantum effects dominate, the information within becomes accessible, which could again allow potentially studying the inside.