At a glance, the black ones appear to be made of granite - this is very tough! You might wonder how they were ever able to make such perfect representations with very hard material 3000+ years ago. And to then polish them so well that the polish still looks good after all this time, as on the picture at the top of that article.

However (and whenever) they were made, once made, these are hard and most definitely do NOT break accidentally. Well, not so many of them as that, anyway. If it is granite, I think you could drop a statue like that and it would break your wood or marble floor, rather than break off accidentally.

Maybe the dangling arms of greek statues fall off over time (the article points out that statues held together with dowels are especially susceptible, vs carved from a single block)

But a lot of these statues have arms by their side. Further, the author mentions chisel marks and describes where a statue was hit to break it apart. I think the 'iconoclasm' explanation is fairly uncontroversial.