If a thousand writers were each given the same very specific story idea, you would end up with a thousand very different stories. A few of those manuscripts could even become bestsellers.
Because each of us brings a unique set of life experiences to the table. We view the world in vastly different ways, have met a variety of people, and incorporate our individual likes and dislikes into the mix.
Just like a time capsule contains tidbits of information relating to a particular society, the things that influence our writing make it individual to each writer.
People. The characters in my book are shaped by the people I know (including myself). Added to those, are individuals who have touched my life via books and media. One of my recent characters is based upon a Jane Austen character who amused me in Pride and Prejudice. Whether the person you create is a positive or negative one, it is likely influenced by someone you know.
Places. The catalogue of locations you've grown up in or visited over the years will inform the settings of your novels. Even if your book is based upon a place you've never been, it is colored by the settings you've known.
Experiences. The vast array of things that have happened to you, whether by your choice or not, will show up in some way in your fiction. A tragic accident in my town left a mark on many families I knew. That experience ended up becoming a short story named After.
Even if you broadcast your story idea to the world, there is no on on earth who could write it just like you. Sure, someone could "steal" the idea, but their execution of it would not even come close to yours.
So, what's in your box? What people, places, and experiences have made their way into your writing so far?