Why is Feature Driven Development considered an Agile methodology?

Question

In several places Feature Driven Development (FDD) is called an Agile methodogoly - e.g. the Wikipedia entry on FDD.

Yet in general, to be considered FDD it seems the following requirements have to be satisfied:

• Coloured UML has to be used (but documentation isn't necessary);
• Instead of pair programming the team is divided by software features;
• refactoring is discouraged or, at least, isn't a task with explicit scope;
• unit testing is discretionary, the team leaders can decide;
• the work flow has to pass through the five FDD phases;

On the flip side it seems to me that Agile is

• UML is an optional tool
• Tests are documentation
• Tests are obligatory
• refactoring is a consequence of the change requests of the customer and it isn't discouraged.

Am I wrong with my understanding of either concept?