I saw the traveling _Gods in Color_ exhibit when it came to San Francisco, which is where some or all of the images in this article come from. I don't think the exhibit glossed over the fact that these reconstructions are speculative, and that we can't know for sure what the originals looked like.

One quote I remember from the exhibit, which I looked up to make sure I got the wording right, was an anecdote about one of the most famous Greek sculptors, as recorded by Pliny: "When asked which of his works in marble he liked the most, Praxiteles used to say: ‘Those to which Nikias has set his hand’—so highly did he esteem his coloring of the surface."

One takeaway from that quote is the obvious: one reason we know that ancient statues were painted is that ancient authors said so. Another takeaway is that the painters, not just the sculptors, were famous, and the ancients recognized that some were better than others.