The company behind Graph Everywhere, Jesus Llevadias, built a business around graph databases after noticing a gap between customer data and how it was being used. They chose Neo4j as the primary tool due to its ACID compliance and ability to handle complex relationships in customer data. By leveraging Neo4j, customers were able to simplify their data models and find connections more easily. The company carefully considered introducing new technology to avoid unnecessary complexity, ultimately concluding that Neo4j was the best fit for their customers' needs.