I will try and answer your questions the best I can.I at one time was involed in dog rescue.
The mileage being requested is for the person to travel with the dog.Persons doing this work goes and picks up a dog then usually takes it to it's home and gets it ready to place in a adoption home.

The airlines charge a fee to transport the dogs but this is alot less then shipping them air freight if a person travels with the dog.This is especially regarding the larger breeds that are over 100 lbs.

I hope this helps answer some of your questions.I would hope you would consider giving any help you can to any organization doing this.It takes a great deal of expense and time.