I have certainly seen first hand how parents teach their children to be racist and rude. It's a disturbing sight...you have to be carefully taught as the saying goes.
On the other hand, this could all be a misunderstanding. The kid was about four, and four year olds haven't learned to filter what comes out of their mouths -- or what goes into their brains. I wasn't there to hear what the kid said, but imagine with me this scenario:
A little boy sees somebody making racist comments on TV or in a movie while over at a friend's house. He might have some African American neighbors with mean dogs (I've had neighbors with mean dogs, and that fact alone made them seem scary and crazy to me. I've also had neighbors who regularly yell obsecenities at each other beginning before 7 AM).
He's just come to the age when he's figuring out that boys and girls are different, and that boys grow up to be men who get married to girls who grow up to be women, and then they'll be mommies and daddies. This is a fascinating subject to kids this age, and they often say they'll get married to some little girl they know when they grow up -- or to their sister or mom. This is a natural stage of child development.
Then, maybe he meets an African American woman somewhere -- perhaps at the grocery store -- and doesn't like the way she smells because she's wearing some strong perfume. He tells his mom he doesn't want to marry her when he grows up, and his mom says, "Ok, you don't have to." She may also support his idea that those particular neighbors aren't allowed to come over to his house for entirely non-racist reasons.
All these things are floating around in his head, and he makes some overgeneralizations and statements with loaded words that he doesn't understand the power of (Have you ever heard a little kid who has picked up a swear word from somewhere and says it only because it gets a reaction from everyone he says it to?). This is also natural for his developmental stage. Perhaps his mom hasn't heard him talking that way yet, or maybe she hasn't had time to sit down and explain just what might be considered offensive to other people, even if he doesn't mean it that way (I remember being amazed at some of the things my mom made me stop doing that I look back on now and feel terrible about). All you have to do is look in the back of any parenting magazine to see a whole list of horribly embarassing things that kids have said or done.
I wasn't there, so I can't be sure this is what happened, but I find this scenario much more plausible than that his mom (in Provo Utah) is teaching him that black people aren't allowed at his house because they smell. Remember that young mothers here are mostly Mormons and/or married to BYU students -- those populations aren't known for being blatantly racist, but they're also very known for being kind of sheltered -- they might not know ANY black people except for the neighbors with the dogs.
Though I don't know what was up with this little kid, I do know that I've been on the other end of this kind of misunderstanding. I was teaching a Hands-on-History class where each girl made a little cloth doll while I told stories about pioneers. I had made body parts for these dolls from seventeen different colors of fabric from pure black to pure white with every shade of brown, peach, and beige in between. When one of the African American girls chose the pure black, one of the other girls smugly said that black people weren't really black and made the first girl feel stupid for choosing that color. To make her feel better, I told the girls that there are indeed some people with skin that is so dark it's black almost bordering on blue (for instance, a guy I know from Africa). I also said that everybody was allowed to make their doll however they wanted, and it was nobody else's business. The girls each chose and sewed on the button eyes, yarn hair, and pioneer dress for their dolls. This was the first sewing experience for many of the 9 or 10 year old girls, and their dolls looked like a child had made them, as they should.
When the little girl proudly showed her dad the doll she had worked so hard on, with its button eyes kind of crooked, and the curly black yarn hair sticking out at odd angles, he tore it from her hands and stormed into the museum. He cornered me and was yelling about how I was a horrible person for teaching racial stereotypes, and that his daughter said that I thought black people looked like this doll (which, I now realize, did kind of look like a pickaninny of sorts). I felt physically threatened by him, and took refuge in another room while my boss dealt with him, but it took me several hours to calm down and feel safe again.
So yeah, the boy at the park might have been carefully taught to exclude smelly black people, but it's just as possible that he hasn't yet been carefully taught to be kind, sensitive, and inclusive yet.