Why not both?

As far As we can tell from modern testing methods- it was common practice based on residue and traces found on many ancient statues- that yes! Many were in fact painted. Periods, cultures etc. vary- some were bright and somewhat fanciful, others seem to be colored in what we believe are more “realistic” color pallets. The “sterile/clean/simple white” we associate with these classic works- isn’t likely what most looked like new. Just as if an alien landed at the Apollo site on the moon- they wouldn’t find an American flag in red, white, and blue- but would find a white flag which radiation (such as from the sun) and other factors over time had made white!

Or perhaps more relatable to many- the same that very old lawn furniture or car upholstery- if not protected from the sun- loses its color and patterns over time. You may never have seen an all white lawn chair or Toyota Tercel interior- but you also haven’t likely seen one that was left in the elements for thousands of years. A decade or two can often be more than enough to make many colors turn almost white.

It goes back further; pillars and statues in Egypt were also painted... and then there's an argument over where they learned how to do that. Dyes were the original purpose of what tade/globalization has become and, in particular, it was things you could use to make blues that made it such. Blue was rare, even rarer was being able to get a guy to make blue+red=purple, which is why purple was considered reserved for royalty.

You can trace it all the way up to printing. White, black, red and yellow are easy. That's part of the reason old comics look the way they do.

There's always a reason to have nude statues