Mary Jane's Cat Supplies

First off I am not planning on breeding a dog/cat, I don't even own one but I was talking with a friend of mine about pet ownership and she said she heard ( she wasn't sure from who) that its healthier and best to have a female dog produce one litter and then neuter them rather than neuter without having puppies. I disagreed and said it shouldn't affect the health or happiness of the dog if she was neutered and didn't have a litter. Are there any Vet's or Breeders that know and why or why not? I know about pet overpopulation and am not advocating it I was just wondering about this question so please don't start attacking me or preaching, I just want an honest answer and to dispel this myth if it is one. (Sorry but I asked this of a pet site and got *yelled* at and accused of trying to push 'puppy mill' pregnancies and being part of the pet overpopulation problem', etc. etc.