Final answer:
Yes, triggers do fire regardless of the method used to save the triggering data, whether it be via the UI, API, Data Loader, or other means. They are designed to execute after their specified triggering event occurs in the database.
Step-by-step explanation:
Triggers are a feature of many database management systems, and they are designed to automatically execute a specified action when certain events occur within the database. The question whether triggers fire regardless of how the triggering data has been saved can be answered as 'Yes'. Triggers are often implemented to maintain data integrity, enforce business rules, and update system logs among other tasks. They will execute following their defined event, be that an INSERT, UPDATE, DELETE, or even a DDL statement like CREATE or ALTER, on the table or view to which they are attached. That means no matter if the changes to data come through the user interface (UI), an application programming interface (API), a bulk data processing tool like the Data Loader, or any other method, as long as the specified event occurs, the trigger will run. It is important for database administrators and application developers to be aware of this behavior as it can have performance implications and may affect the execution of batch operations.