For the purposes of communicating with larger audiences, I'm assuming the general experience with dogs, which is typically as a house pet. You're correct that a

For the purposes of communicating with larger audiences, I'm assuming the general experience with dogs, which is typically as a house pet. You're correct that a free working dog is a different scenario, but qualifying the idiom loses something. I don't see "free as in puppies suitable for work you can make practical use of" catching on. I am a dog person, for what it's worth.