Short Answer: No, Creatives aren't born, they're created over time and in the right environment.
It's easy for people to say, "you were born with it; you were born with the gift of being creative." My typical response is that it has nothing to do with being born with anything.
Growing up, I was in an environment where my mom and grandmother always encouraged me to doodle and draw. So I did. I brought daily and went on this way from the age of one or two up to today.
Anyone can become a creative person, and that means different things for different people. Some want to be able to draw, paint, sculpt, carve, record, or photograph. Each and everyone one of these skills can be obtained through hard work and dedication.
A great way to look at it is this, look at people who play an instrument, are great public speakers, or are very social, skateboarders, business people, etc. All of those people weren't born with fundamental skills, and they worked hard to learn and to hone in on their craft.
If you want to become a creative person, you have to put yourself in an environment where you can succeed. For instance, if you want to learn how to draw, go out, buy yourself a couple of reams of copy paper and some pencils or pens (your choice) and start drawing until you are out of paper. Keep at it and keep creating, and you will get better and better over time.
To help illustrate my point, here's a link to my old DeviantArt page that I started back in high school and continued to post work through college. You can see a progression of some of my earlier works of "art."
In complete transparency, my old work sucked… horribly.
But I didn't quit, I kept going, I kept creating, and today I feel like I'm a lot better now then I was back then. It's somewhat proof to show that your skills will grow over time and with practice.
No one is an overnight success, but you can be a success if you put in the time and effort. The cool thing is that this goes beyond just being creative. You can use all of this that I talked about here to fuel any and every passion that you have, whether it's being creative or being an entrepreneur.