I consider myself a creative person, but I believe that all people have some capacity for creativity, despite what individuals believe or profess about themselves. I think my opinion about "creativity" is centered in how frame where creative thoughts come from, and what creativity truly means.
To me, no thoughts or ideas are truly and strictly original. There is always a wisp of something that came before, some outside influence, inspiration, or impetus. Creativity is more a unique or new combination, use, process applied to old materials, thoughts, or modes of action. Things can be discovered, as in a new plant in the rain forest or imaging the far reaches of the universe, but creativity is not discovery. The materials of life on Earth have been in existence far longer than I have, but I may find some new way to use them.
Artists, who are usually the first "creative" people who come to mind, use media that generations before them have manipulated. The creativity comes from drawing on inspiration and experience to make something unique. Alternately, artists often take materials that have not traditionally been used to create art, such as lego blocks (that's a topic for another post) and make them into sculptures the same way ancient artists worked in stone.
I hope that the paradigm relating to who is creative and who is not can change, but that will only happen if those who claim to lack creativity allow themselves take the old around them and make something new.
Here's a Stanford Professor who agrees with my point of view. He's talking about creativity as it relates to entrepreneurship.