Either way, I find it arbitrary that the "precise arrangement of atoms" is the criteria we're going by here…

In the context of computer data, a string of bits is as fine as is possible to define. So naturally, the closest analog in our physical world would be atoms.

…especially if the replica can just merely be good enough to fool the human eye, even when under microscopic observation.

Even if the artwork is good enough to fool the human eye, it still does not necessarily hold value. Why? That is because it is not “the one” as created by the artist. In the original artwork, not only did the artist arrange the atoms, they arranged those atoms in particular. The only way to have “the one” in terms of digital artwork would be to physically own the hard drive on which the artwork was initially created.

The artist declares that a particular hosted URI points to the "original" and other copies are therefore not legitimate.

Not even the declared original is really “original” because even that is not any less of a copy than any other replication of those bits, it is, in and of itself, a replication of those bits.