Ah, did you look at the second link?

It is somewhat more difficult to understand the “chromosome tangling hypothesis.” We recently found that asbestos fibers including crocidolite are actively taken up by several different kinds of cultured cells. Furthermore, those fibers enter both the cytoplasm and the nucleus. In this situation, asbestos fibers may tangle with chromosomes when cells divide. Whether there is a specificity of tangling for any chromosomal region is the next question to be addressed.

Which comes with this image:

Granted there isn't a lot of experimental evidence for this (that I can find, anyway), but it makes sense that tiny little silicate needles that get absorbed by the nucleus interfere with the chromosomes both mechanically and chemically.

I also found this:

A normal (A) and an abnormal (B) anaphase from asbestos-treated Syrian hamster embryo cells. Note the asbestos fibers (arrows), some of which appear to be associated with displaced chromosomes (arrowheads) in the abnormal anaphase. Reproduced from Hesterberg and Barrett (42) with permission.

Asbestos fibers are observed in the mitotic cells and appear, in some cases, to interact directly with the chromosomes. From these studies we propose that the physical interaction of asbestos fibers with the chromosomes or structural proteins of the spindle apparatus causes missegregation of chromosomes during mitosis, resulting in aneuploidy.

https://www.researchgate.net/figure/A-normal-A-and-an-abnormal-B-anaphase-from-asbestos-treated-Syrian-hamster-embryo_fig1_20488222