I'm by no means an expert on this.. only a lowly premed undergrad, but I do have PCOS and I know my endocrinology at least in that regard.
What I'm thinking is that heightened insulin levels actually cause an increase in the amount of androgens (male hormones) the ovaries produce. This causes abnormal follicular maturation (the growth and passing of the egg).
I'm sure people's bodies adjust to this if it's been their way of life for a long time. Buuut once the dieting and all that starts really affecting things like insulin levels, it could throw off the hormone levels and as a result, it might throw off menstruation cycles.
This is all guess work on my part - I don't really know why alli would cause periods to be nonexistent.. if anything I'd expect the opposite.