I have to go along with the idea that Annie got pregnant by Ben and then died.
This may explain why Ben helped with the purge. Dharma could not save Annie and therefore Ben blamed them for her death.
To add another thought, maybe Richard gave Alex to Ben as a way to replace the child that he lost along with Annie if he would help with the purge. I do not mean that Richard is Alex's father, just that Richard could get Alex and give her to Ben.
Oooh! Now there is an idea. I feel that Ben and Richard are not on the same wavelength. Just look at the history of each of them involved with the island. Richard is something different from Ben, and as he has shown, not one of Ben's puppets. He has his own thoughts and opinions. Now let's look back 16 years. We don't really know WHEN Ben came 100% over to Richards side and killed his dad during the purge, but we do know that Danielle ended up on the island. So. Let's say that Ben is still working with Dharma, Richard is still part of the natives, and Danielle just crashed. Richard appeared to Ben the first time right after the whispers by the fence. Didn't Danielle say she heard whispers before Alex was taken? If these Richard is somehow in tune with the whispers, RICHARD could have been at the scene of the crime. Of course, most of the times we hear whispers Richard isn't around. Anyhow, I could definitely see Richard using Alex as some sort of leverage- like giving Ben a chance to create another childhood. Or something.