True, though it's really important to ask how they will do it. I have read that some vets use a "heartstick" method that is painful and not all that fast.
I took a chicken to the vet and they said they were going to use a gas overdose and that I couldn't be in the room when they did it. While the vet seemed nice, I have always regretted not seeing exactly how the chicken was put down and worried that maybe they didn't do what they said they would.
I am gripped with anxiety about euthanasia because I'm always so scared that I will mess up and cause the animal more suffering. At this point, though, I have watched my dad use a hatchet to decapitate two of my beloved chickens when they were terminally ill, and I think the next time I will attempt on my own.
Agree with everyone who says that the fastest method is best. I know it seems "nicer" to do something bloodless like an overdose or whatever, but the "nasty" method of beheading/cervical dislocation/quick bleedout are more humane.
I do remember someone talking about a carbon dioxide box system that is humane but just takes a very long time.