My favorite is the following scenario that's happened to me at multiple clinics in some form or another:
Nurse: "Well, I don't think there is anything wrong with you, but lets do an extra scan just in case"
Me: "Sounds good. How much does the scan cost?"
Nurse: *looks aghast at such a request* "You have insurance, why would you care?"
Me: "..." *thinks of explaining how the cost ends up being payed by me in either case*
Another experience calling the Hospital after having a child:
Acc = Hospital accounts receivable personnel
Me: "I've received 7 different bills over the last few months. I would really like to pay off any balance so I can budget appropriately"
Acc: "You have paid off all balance with the hospital"
Me: "So, I shouldn't receive any more bills for the birth?"
Acc: "I didn't say that. You will just have to see if more bills arrive."
Me: "How will I know when everything has been billed?"
Acc: "I can't imagine bills arriving next year."
Turns out the hospital, nurse midwives, doctor, anesthesiologist, etc etc etc. all bill separately and don't all put their bills in any timely manner. Took 12 months for all the bills to arrive from my last child's birth.