I would not expect to see broken off pins as that likely would have involved a great deal of force.
However, use a magnifying glass to take a close look - could have been a defective pin(s) - especially if the pins do not move and are different heights.
Or the entire assembly was not made correctly.
What about the wires going into the header - do they "slip" in and out a bit?
Be careful checking. The wire could come completely out.
Were/are you installing a replacement fan?
For example:
Replacement fan example