OP, given the responses here you can see why your SIL doesn't tell people she is unschooling.
I first heard of unschooling about 6 years ago when we moved and discovered that the family next door was unschooling their children.
Like a PP mentioned though, there are those that unschool well and those who don't. Unfortunately, those that don't do it well are usually the focus of these types of stories. Our neighbors took their children's education very seriously and they were thriving. The youngest did have some problems, but it was due to a disability and not the education he was getting at home. If done correctly, it is actually quite a bit of work for the parents. For example, their dd was very intetrested in the African Savannah. It is easy to see how you can fit in science and geography. It is also fairly easy to get some history in there as well. They read a lot of great historical and non-historical novels. Their art projects centered on different animals in the region, etc. The parents, however, had to make up their own math problems, etc. Some of it involved calculating area, distance, etc. Others were more involved.... How many areas equal to the state of Florida could you fit in the African Savannah? Driving 60 mph, how long would it take to drive across the Savanah? Things like that. Now these were sometimes done during a family game time or something, so they were often playing games, but they were definitely learning -- and learning a lot.
We are a homeschooling family. We prefer a more structured method of schooling, but also incorporate some unschooling ideas during slower parts of the year. Even then though, we don't stop our math. For example, the girls will pick and animal or a country or a time in history, and we will study it for as long as it holds their interest.
See to me that isnt unschooling. Thats homeschooling without a solid currirulum. The parents still teach and make up problems. The kids may have chosen their interest but the parents are still involved and still guiding them. No way is a kid going to sit down and say "Today I want to figure out the calculation of how many miles we have to travel" or whatever. Especially if they dont they have guidance.
The family that was featured on GMA let the children do whatever it is they wanted to do and were darn proud of the fact that they usually chose nothing.