I mean, I kind of disagree with the assumption that bright colors immediately mean horrible; especially when we're comparing to a dirty ruin of a mosaic for the "real" color. That's probably gotten less saturated over time too.
But that aside, I do think the author has a point here. Many people don't know ancient statues were painted at all, an academic creates a reconstruction based off of the color traces that survive to show otherwise, but likely only the underlayer, then that gets dumbed down to "this is exactly how the statue looked to the Romans!" because that's counter-intuitive and therefore more likely to get attention. It's not just statues too, but in pretty much all popular media that derives from academic subjects.