Of course this is anecdata.
Ours UCSF, pressured and pressured my wife to breastfeed even though her milk was having massive problems coming in. Instead of allowing formula they only allowed donor breast milk supplementation by tubes that were taped to my wife's nipples, to attempt to prevent "nipple confusion".
The way it was explained to us, the idea is to continue to stimulate milk production while supplementing. We used it for a week until production was sufficient. I personally enjoyed this as it allowed me to be more involved and removed the stress of knowing if we were feeding our child enough while still getting what we could from breastfeeding.
We definitely had a great hospital. With all the stress and lack of sleep, I'm not sure I would've kept calm if they'd imposed stuff that way. Not letting you the choice of using formula when using the breastfeeding aid seems crazy.