I'm sure whoever gave those standing orders would agree that taking care of the emergency was the higher priority. The quasar wasn't going anywhere.
But neither was the emergency.
There would have been no benefit to hurrying: Kirk was to make a
rendezvous to deliver that medicine to the next link in the chain that would end with the people in need. Two things are apparent from that setup, and rather dictated by each other: there was no option of him flying directly to the patients, and the next flight wouldn't depart any earlier even if Kirk hastened his own schedule.
So Kirk had three days to burn, and those were his to burn. It's not known whether he got proper scientific return out of it, but at least it created no delay or other downside for the people in need of the medicine.
Timo Saloniemi