Can you explain this part of "The Three Burials of Melquiades Estrada"?

I need some help understanding a part of the movie - this has been
nagging at me ever since I saw the movie. I can't figure out why the
supposed wife of Melquiades, when Tommy Lee Jones finds her in Mexico
and shows her the picture, says that she doesn't know anybody named
Melquiades, that she doesn't have a husband in the USA, etc., but
says, "Why do you have a picture of me and my children?"

I'm confused. Why did Melquiades have the picture, then? Or was she
lying?