First off, ultrasound measurements are notoriously inaccurate, especially in late pregnancy when baby is cramped up and it's more difficult to get good images to measure. Babies also come in different proportions. Anecdotally, my perfectly healthy DS was in the 17th percentile for weight, 25th for length and 50th for head circumference at birth.
In my very personal opinion based solely off what you've said, it sounds like they just want to get that baby delivered and open up space in their practice and if they can do it on a timeline convenient to them, all the better (for them). She's signing up for a cascade of interventions if this induction doesn't go perfectly well. If the bulb catheter doesn't work, will she be immediately sectioned? If the pitocin doesn't produce the textbook contractions will they let her body rest and try again in a few days or immediately section? What "harm" could come to her baby by putting off an induction another week (in reference to the ultrasound findings) versus doing it sooner? These are questions she may want to ask her provider, at the very least to know what to expect.
As for natural induction methods (which only work when the body is ready), I would very highly recommend a warm bath, walking, eating pineapple or spicy foods, sex and nipple stimulation. Of course there are more aggressive methods like castor oil but these aren't entirely without risk and discomfort. If you do a quick thread search, you should be able to find them quite easily.
Best of luck to your sister, and lots of luck to you as well with encouraging breastfeeding and being a great support person (which it sounds like you already are!)