Anyone can be a writer. They just either don't do it, or can't brainstorm decent story ideas. These prompts are ideas I could never continue. You may use them, and take credit for it. I only gave the idea. If you use a prompt, you deserve the credit for continuing it.
I always think of the most random poems when I'm bored. Some of them are actually good, so it would be a waste if I didn't write them down. I also think of them when I'm upset.