When I was pregnant with my 5th child, I had an ultrasound done at 4 months because my normal work pants still fit and I was concerned. (And I am neither hugely obese NOR in such great shape that a pregnancy wouldn't show.) With vests on, as in the pics on DU, I probably would have made it through most of my 6th month without comment.
I worked all day Friday...a full 8 hours, and was called back in that evening to fix a leak on a dialysis machine. My water had broken the night before, so I was wearing pads all day, but was not in hard labor by any means.
My oldest took me to the hospital about 11 PM, after I'd gotten someone to cover call for me. My youngest was born about 3:30 AM. By 3 PM, I was back home. My older kids were great about helping with the baby, but not very interested in cooking, cleaning and laundry.
I did wait 6 weeks to go back to my job, but that was because no daycare would take a baby younger than 6 weeks.
I have no doubt that Mrs. Palin did exactly what she said she did.
Besides, the pic on DU has the oldest daughter, who is NOT wearing a vest and is obviously not several months pregnant.