Many don’t fill prescriptions for the general public but will fill for discharge meds. The issue comes up in NICUs fairly commonly as some of the relatively common NICU discharge meds (like caffeine - used for apnea of prematurity) is not typically stocked at the local CVS. And is expensive (although I still do not understand why).
Mama Zappa, maybe my limited experience with NICU nursing staffs has given me too good of impression overall.
Mine as well, actually - the vast majority of the nursing staff at least during our stint there (and during the times I volunteered at a NICU many years ago) were very caring and devoted, and went out of their way to communicate with the parents. Which was why our situation (total stranger telling my my daughter was being discharged, another total stranger “handling” the discharge) was such a shock. Admittedly our daughter was not one of the more fragile babies, but it really felt like we were booted out suddenly and were probably missing a LOT of information we needed. We were terrified. This was why the idea of the NICU dropping the ball on preparing the OP for needed meds etc. was not too hard to understand 
After reading the blog, I am reinforced in my amazement at the fact that absolutely every time there is a breakdown in customer service, it is always the customer’s fault. Man, customers truly suck.
A while back, we were at a restaurant. We had a great meal and good service, but when it came time for the check, the waitress was not to be found. After 20-30 minutes she reappeared and apologized, saying “sorry, I was in a conversation with my manager and lost track of the time.”
At the time I was annoyed, but in retrospect, the waitress actually took responsibility for her mistake. A rare thing, indeed.