Nothing could be further from the truth.
For puppies to develop into dogs that are comfortable around children, they must be exposed to children during their critical socialisation period between 8 and 14 weeks. The more positive experiences the puppy has when around children, the better. This could include having children feed the puppy treats, rewarding simple behaviours such as a sit or coming to them. Ideally an adult should provide reassurance and maybe more treats when kids make their high pitched noises and run around wildly, as they will.
At the same time, children need to be taught how to behave appropriately around dogs and puppies. Whilst you can try to get your dog to accept things such as patting on the head and pulling his tail, it is very advisable to teach the human youngsters that dogs are to be treated gently at all times, and to protect the dog from unpleasant handling.
Omitting to do any of the above can easily lead to problems. Yes, many dogs end up being tolerant of children even without proper socialisation, but that is no more than luck, and grossly negligent.
The only thing worse than omitting proper socalisation is subsequent punishment of the dog if he growls at a child. One owner proudly informed me recently how his dog now promptly leaves the room when his child enters, after having been severely punished for growling at his child previously. I know who is going to the blamed for the disaster that is likely to occur should this dog ever find himself inadvertently cornered by a child. Unfortunately it won't be the owner.
The other aspect of "perfect family dogs" such as Labradors is that they rarely classify as anything other than tanks on legs in their first few years of life, and, without proper impulse control training, possibly for the rest of their lives. Labs show up in relatively large numbers at the RSPCA, and their "giant puppy" temperament could be one reason. Children under eight will find themselves taken off their feet by the happy Lab pup on many occasions, surely not quite what the parents had in mind when they completed their family with their four-legged child.
So the unsurprising conclusion is that most dogs can become the "perfect family dog" and be tolerant or even appreciative of children given correct positive training and conditioning and extensive socialisation. As for the breeds, it is much more important to be aware of what they were bred for, and so what their likely inbuilt behaviours are, than supposed "kid-friendly" characteristics. Read some breed-specific training tips here.
Bringing a dog into a family is a huge commitment and poses many challenges, particularly if the children are small. Tips on how to get it right will be the topic of another blog post!