Maybe Penny's dad is part of the Dharma Initiative.
Anybody know when Ben murdered all the Dharma people? Was it before or after Desmond washed up on the island in 2001?
Either way, when Ben & co. killed off Dharma, I think they had a few other Dharma people who turned their coat and/or cut deals to survive -- among them, Mikhail & Clancy Brown's character. Clancy was stationed at the hatch (Ben and his dad went there to drop off the beer), and allowed to stay, because the button has to be pressed. Desmond was either already there (though why was Clancy lying to him before the attack?), or washes up later, and they just lie to him to keep him there without having to kill him.
Mikhail gets left at the satellite uplink, either to keep feeding Dharma fake info ("Yeah, everything's fine here. We're all fine. How are you?" Except they're better liars than Han), or to talk to some allies (a faction amongst the Initiative?). They certainly still have sources in the outside world; witness the videotape & files on the survivors.
Then the button doesn't get pressed, and the Anomaly starts to go off, bringing down 815 before the override is activated. Lucky for Ben, what with his spinal problems and all.
Then the button doesn't get pressed at all, and the Anomaly really goes off. Now Dharma totally loses contact with the island, and they begin searching for the island. (Or, if Dharma wasn't being strung along by Ben & co., now they suddenly have a fix on the island's general location.) Except they need a constant beacon from the island to really pinpoint it, and Ben is either jamming whatever beacon was there, or the anomaly blew it away. So they can't pinpoint the island, though they are in the neighborhood.
One of their pilots stumbles into the island, and manages to survive. She has a picture of Desmond & Penny -- because Dharma knows he was on the island, ? Maybe Penny's dad is part of the Initiative, and gave 'em the picture. Maybe she was expected to crash, due to the island's effects; ergo the slightly unusual (AFAIK) sight of a helicopter pilot with a parachute.