To answer your question, NO.. It's NOT OK. But I don't think that the people owning dogs are taking their dogs to non dog owners homes and having them do their business. I think that most dog owners are responsible.
I think the OP is having a problem with someone THEY live near. But I really doubt that it's an issue. Most of the people on this thread seems to me to be VERY concerned about this.
I have dogs and I agree that it's NOT OK. And to be honest, I don't want someone to bring their dog to my yard to do his duty... and if he does please have the courtesy to clean it up. But I also know that dogs are ....... dogs. They don't know MY grass from YOUR grass. So if by chance a dog does get confused. Just clean it up and carry on.
I'm pretty sure that most dog owners would agree that a dog should not be encouraged to do their "duty" on someone else's yard.
Except Fumar... He LOVES dogs!