The role of Product Designer is to make coherent the set of stories
from a vast set of customers. This role is important when doing
products where one in-house customer can not represent the target
market.

In this case, the Product Designer plays the role of Customer in XP.
The Product Designer may, however, come from the customer's problem
domain. Or, the Product Designer may be a design expert who steeps
themselves in customer contact. The trade-off is which risk to take:
teach a customer to design, or teach a designer about the customer
needs. (This last point came from an InterviewWithKent).