In regard to breast pumps:
It's not as easy a solution as it sounds. Say you just had your baby a few weeks ago and are getting out of the house for the first time. Using a breast pump to express milk and feed it to the baby in a bottle is actually a bad thing to do the first few weeks. Artificial nipples may cause nipple confusion in the baby, starting a whole round of problems breastfeeding, which are not in the best interest of the baby. A baby needs the plentiful nourishment of his or her mother's milk, and nipple confusion may cause latch on problems that will affect the quantity of milk received, and thus, the baby's growth (a problem totally preventable in such a case!).
As for older babies, pumping might be an option if the mother can actually afford a breast pump. They are very expensive!! Buying one just for the sake of pumping a few times is definitely not worth it. Not only that, but substituting a bottle for the breast will undoubtedly lead to a decrease in milk supply. Milk production is based on a supply-and-demand system activated by a baby's sucking. So, if you pump ahead of time and then skip several feedings, your milk supply will suffer, and thus, again, your baby's growth.
Finally, I also agree with the previous comment that the woman on the show against public breastfeeding has an issue she could not admit. She clearly has an issue with an infant sucking the breast of a woman (a sexual issue), because it is still unacceptable for her to see a breastfeeding baby without seeing even a sliver of the woman's breast. Her issue is really with what she KNOWS is going on (an infant sucking a woman's nipple), not with what she can ACTUALLY SEE (the back of a baby's head positioned to the side of a woman's chest).
IT IS ALL IN THE EYE OF THE BEHOLDER. Think about it.
(Obviously, this does not apply to women who expose their breast before getting the child ready to nurse. As a public breastfeeder, I know it is possible to be more discreet than that.)