How to deal with an injured pigeon

Living near the South Mountains means having to deal with birds, scorpions, rabbits and all kinds of wildlife that I never saw when I was living in Tempe. Yesterday I came back from a shopping trip and found a pigeon on my doorstep. There was pigeon poop and feathers everywhere and when I opened the door, the pigeon wouldn't move. Worried that it might be injured and in pain, and not knowing what to do, I went online to find the local SPCA phone number. So there I was, making a few calls when I strolled back to the front door and found a little girl, standing on her scooter and staring intently at the bird. Both of us stared at the bird some more and then she spoke.

Little 10 year old (LTYO): It's injured.
LTYO: I think his back is broken. And his wings.
Me (not able to think of anything else to say): Yeah... what do we do about it now?
LTYO: Well, just kill him.
Me: What! (my eyes almost popped out)
LTYO: Yeah, it's just a pigeon.
Me: Uh...um.. how would we do it?
LTYO: Oh, just throw a big boulder at him.

When she grows up, I'm moving to the next town.

P.S. The pigeon eventually walked away. The only advice the AZ Humane Society could give me was to put it to sleep. I think some coyote must have done the needy.