Earlier quoted context omitted.
If we can confidently confirm that 1) there are leftover vaccines, 2) good-faith efforts were made to administer them to the target audience, and 3) there were leftover vaccines that were definitely otherwise going to go to waste then I'm 100% fine with people administering to their contact list. I'd rather that 1000x over than unused vaccines be tossed into the garbage. We all lose with unused vaccines.
It's just poor design to allow for good-faith. It's too easy for a bad actor to artificially create "leftover" doses to give to friends and family. Just don't allow doctor discretion and organize better for the next day, problem solved.
How? If X people made appointments in a day, then exactly X vaccines should be distributed for that day. Leftover vaccines will only be distributed after all those appointments are over, so it is impossible for any of the X people(assuming they arrived on time) to lose their vaccine.