I'm uncertain about exactly how common this intuition is, but it seems that fairly frequently people find the idea that a program - an artificial intelligence - could be creative is ridiculous. The thought that we can develop a cognitive model of something as uniquely and irreducibly human as creativity seems absurd, right? How could a model or program ever account for works like this;
The problem with such an intuition is that it appears that cognitive models of creativity are possible. The music playing in the video linked above was written by a program, trained by its creator - David Cope - to write music he enjoys listening to. There are some good links about theories behind cognitive views of creativity and an example of another artistic program, AARON, on this page.
One of the earliest projects in artificial intelligence, DENDRAL, was even explicitly designed to generate and test scientific hypotheses. I would call that, too, a form of creativity, although much of the literature on creativity tends to focus on the artistic side rather than the scientific one. How different the two forms of creativity are, I'm uncertain; food for thought, perhaps.