Simple: The Open Hip Twist includes the Fan.
The 'Fan' as a figure is nothing more than a simple way of describing a method for achieveing 'Fan' as a position. Many figures which end in Fan position therefore can be said to include the Fan (figure).
Because the ballroom dance syllabus is a series of figures built from many of the same basic building blocks, there's no shortage of similar or overlapping figures such as the one above. That's actually one of the nice things about it... once you learn the basic building blocks, you don't have to keep re-inventing the wheel every time you work on a new pattern. As you work through the syllabus, you'll notice that most of what you learn is based on something you already know.
Other examples of overlapping patterns:
1-3 of a Natural Spin Turn in Waltz is really just the first half of a Natural Turn.
7-9 of a Natural Spin turn is really just the second half of a Reverse Turn.
4-6 of a Basic Weave is the same as 4-6 Weave from PP, which is also the same as an Outside Change.
4-7 of a Rock Turn in Tango is really just a Back Corte (which always made me wonder... why is Rock Turn listed before Back Corte in the syllabus?)
Anyway, you get the idea.
Jonathan