To clarify for those not from the US: an MPAA "R" rating means that children under 17 are not admitted unless accompanied by an adult. http://www.mpaa.org/film-ratings/
In other words, it's movies we're okay with kids seeing - but they need to see it with an adult, presumably one who knows it's something this specific child will be able to handle.
I read this and thought "I'd be amazed any parent would let their child see any movie by themselves".
Then I realized I did it all the time with friends when I was 10-16 and we had a cinema 3 miles into town we would walk to, and I am only 24 this year. Its like the American Family went over-protectionist deep end in just this decade or something, because my brother who lives with his mother can't even walk to the school bus stop down the street by himself without it potentially resulting in a police call.
In other words, it's movies we're okay with kids seeing - but they need to see it with an adult, presumably one who knows it's something this specific child will be able to handle.