I don't know if this is totally true. Lucy, a dog that is traveling around to visit servicemembers came to my base today and she is awesome. She's a chocolate lab mix that loved playing catch with us. I will ask her handler, a veterinarian if she knows of this. There is a company that ships pets back to the states and I assisted my friend in sending his company's mascot Siggy (real name Signal) back to his parents house. Rabbies is really bad here. We had a member die after getting bitten so the chances of some of these dogs catching rabies is good here. There could be several reasons why the dogs are getting put to sleep but the cost of sending them back to the states is generally not a reason because they are on orders just like we are.