Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle? By "human-sized lab" I mean a lab the size of the International Space Station, say, with typically-sized lab equipment. I also mean the absolute kind of (event) horizon, not the apparent kind.
The #1 answer at this question says:
For large enough black holes, space is still weakly curved at the event horizon, so of course we should expect that normal physics still exists there. An infalling observer wouldn't experience anything out of the ordinary when crossing an event horizon.
This suggests that the answer to my question here is "yes". However, when I asked a question involving such a test, the highest-rated answer with 23 votes clearly says "no":
The equivalence principle only allows you to transform to an inertial frame locally. This means that if your spacetime is curved, then the falling observer can only choose Minkowski coordinates for an infinitesimal region around her.
I've seen this contradiction many times elsewhere. Certainly the EP has actually been tested to high precision in larger-than-infinitesimal labs. Yet once one talks about testing the EP in a lab falling through the horizon of a black hole it seem respondents in that case think the lab must be infinitesimal in size, so that the EP can't be tested in any practical sense, even though "An infalling observer wouldn't experience anything out of the ordinary when crossing an event horizon" if the black hole was sufficiently large.
I understand that the EP is strictly true for only a point in spacetime. But that hasn't prevented it from being validly tested to high precision in a larger lab, where the tidal force in the lab was weak enough that it didn't change the result at that precision. I'm not asking about testing the EP to infinite precision, nor am I asking about a test involving a black hole of any size, like one where the lab would be spaghettified by the tidal force before reaching the horizon. That's why I qualified the question with "in principle".
Also note that I'm talking about a test being done as the lab equipment (temporarily) straddles the horizon, not a test limited to one side of the horizon or the other within the lab. A test using equipment straddling the horizon wouldn't be allowed according to the other answer with 23 votes, which says:
The infinitesimal flat patch in which you're allowed to play with the EP does not include ... anything beyond the horizon ...
I don't see how a test of the EP would be invalidated due to the equipment straddling the horizon.