I thought this also. I do not know who comes up with article titles, but it should be left to the semi-literate.
They could have easily avoided the ambiguity by stating it as follows:
Boyfriend of grinning woman...At the cost of two additional characters we discover who is grinning. I'm sure the arrested boyfriend is not grinning now.
Wouldn’t “Boyfriend of Grinning Woman” be more passive language than “Grinning Woman’s Boyfriend?” When I was writing my thesis it was drilled into me to avoid passive language whenever possible.