The conclusions drawn by that particular study are definitely premature and inconclusive.
I would really expect the 438 women out of 18,555 in that particular group (which is around 2%) is related to LOW FAT overall dietary choices, and not necessarily with just low fat dairy choices.
Coorelation is not causation, and this seems like it's just one of those things good Doctor Chavarro and his colleagues threw together to get published.
Publish or perish.
I've got to say that after one reading of the "Livin' La Vida Low-Carb" blog, I am extremely underwhelmed with the quality of information.