I agree with you, if a dog runs outside and out the door I would do anything I thought would bring him or her back, treats or whatever. The safety of the dog is more important right then, rather than the protocol of whether to give a treat or not.
I would do whatever it took to get my dog back. We have a busy street and if ours went out the front door they could run out in traffic and as I said I would do anything to get them back.
Jackie