Aren’t intelligence tests limited by the intelligence of the people who create them?
Consider a Rubik's cube: You can mess it up in a few moves a lot more easily than you yourself can solve it, in the same number of moves. How many moves deep can you solve it, using only that many moves? (That is, if it's three moves deep, can you solve it in three moves only?) Anyone can give the cube twenty random moves, but very, very few people could solve it in 20 moves, or say "This configuration is exactly 20 moves from the start."
There's more to intelligence than Rubik's cube, but I myself have thought about your question before, and I find it interesting.