Since an "arbitrary piano" is tuned by turning screws, like simpler string instruments, the only pitches that it cannot be tuned to are those that fall outside the range of each string. Departing from the usual inharmonically tempered 12-EDO tuning would just sound strange, possibly outside some piano tuner's professional comfort zone.
And that isn't a nuanced opinion; a common one among rigid materialists. Its not the best piano for a stage, but I am sure it could fool your ears in a recording. Morpheus would think it was a piano too. "What is real? ..."
You were responding to a comment about how difficult it is to achieve an arbitrary tuning in a piano by bringing up a software piano. It’s a non-sequitur.
Alice: “I have this piano that I need to tune, but tuning pianos is very difficult and I don’t know how”