The same in whatever sense you want to compare the art rather than the creators. Pollocks try to convey the action and emotion of the creation process. Our hypothetical copycat lacks that higher level meaning, even though they've created an otherwise similar physical product.

As an aside:

    ...art should be able to come from anywhere and anyone.

is an immensely political view (and one I happen to agree with). It's not a view shared by all artists, or their art. Ancient art in particular often assumes that the highest forms of art require divine inspiration that isn't accessible to everyone. It's common for epic poetry to invoke muses as a callback to this assumption, nominally to show the author's humility. John Milton's Paradise Lost does this (and reframes the muse within a Christian hierarchy at the same time), although it doesn't come off as remotely humble.