I believe they do, for many reasons. Unfortunately it can undermine a new mother's will to breastfeed her newborn.
But you don't have to take my word for it. The New Born Baby blog has a recent post about hospitals and the way they handle breastfeeding. It's a really good read, and not too long. In the post they mention the Baby Friendly Initiative. I learned a lot about this initiative when I attended the Utah Doula Association's Conference recently.
The Baby Friendly Initiative is intended to help hospitals transform their infant feeding programs to more fully support breastfeeding and only offer supplemental feeding when medically necessary. This initiative is amazing, and I hope more hospitals will strive to become officially Baby Friendly. Right now, only one hospital in the state of Utah has achieved Baby Friendly status.
One big hurdle for most hospitals is that the formula companies give them free infant formula, which they lose by becoming Baby Friendly. However, the representative from the University of Utah Hospital that spoke at the conference I attended said that they found when they renegotiated their contract with the formula companies they were given lower prices on adult formula and the cost of formula for the hospital as a whole remained the same even though they now have to pay for infant formula. What they thought would be the hardest step turned out to be one of the easiest.
I fully support breastfeeding and the Baby Friendly Initiative. Please take some time to educate yourself about these programs and issues.