I've had various levels of urgency in my surgeries... some were scheduled a couple months out ("this cyst could burst, but it's it critical and can wait, just be careful"), some a few days (that was my gallbladder, five days in the hospital total, surgery was a couple days in), and once was immediate (an appendix about to burst). I'd say only that once was truly an emergency, and is the only one I'd call such. The gallbladder was definitely urgent, but not seriously life threatening like the appendix was. The cyst was bad, too, but not nearly as either if the other two. And neither it nor my gallbladder were emergent. Urgent and emergent are in fact different things in a medical setting! Which I'd guess this lady doesn't know.