The shorter stature correlates with earlier puberty regardless of the cause, because growth hormone levels decline as the reproductive hormone levels increase. That’s the kind of thing that’s easily studied.
As far as the cause of early puberty, there are a lot of elements to consider, and scientists can only investigate so much. Many hypotheses have some support, but far short of proof.
I tend to suspect environmental estrogen as far as declining age of puberty for girls, myself.