Misleading title is misleading.
The detailed study found that wives or girlfriends were pleased when their partner showed emotion because they believed it demonstrated a healthy relationship.
It says that women are happy when men show an interest in their feelings and in communicating their own feelings.
Men in today's society are typically told that they shouldn't show emotion ("Men don't cry", etc). Therefore when faced with a difficult circumstance, men tend to clam up. Inevitably, this resistance eventually breaks down, which leads to them breaking down. The article says women are happy upon seeing this because it shows that the man has emotions and does care about the difficult circumstance the relationship is in.
Which I wholeheartedly agree with, and find it amazing that they had to conduct a study to figure this out. I can't agree with their conclusions though: it's not that women enjoy it when men are unhappy, it's that women enjoy men trusting them enough to communicate those unhappy feelings.
(Who wants to bet it was mainly men who conducted this study?)