Whether it requires a dedicated server for the database, you need to consider its application importance, security, availability, performance, and manageability. Here are some thoughts for having a dedicated database server:

Application Importance - If this database supports a critical application, why can't you afford a dedicated server for it to generate more revenue or benefits for the company?:-P

Security - If you want to avoid unrelated people to potentially view the data, dedicated server is a choice.

Availability - The other database instance(s) on the same server may be unstable and requires frequent server reboot that reduces your database availability.

Performance - Your database instance may compete computer resources with other instances that may cause undesired performance to your database.

Manageability - It require more coordination for many things in a shared environment and this coordination is not always an easy task.