Yeah that is strange. Who wouldn't want to see their own work? At least to try and get better at it.

You're as obvious as Quentin Tarantino's foot fetish.

that's what writers and directors are for to tell the actors what they want from them

That comparison makes no sense. The equivalent of what you're describing is an apathetic writer writing what someone wants them to write. Sonya Walger isn't the painter. She's a piece within the painting.
She only has to know the context of Penny's relationship with Desmond, and she does know it beca2000use it's all in the scripts. Watching the show might make her enjoy the show, and maybe enjoy the Desmond character more, but since all of her scenes are with Henry Ian Cusick and her character doesn't really intersect with the main story (nor is she supposed to know any more than what we see of her in the show), she doesn't need any additional context to complete an inspired and genuine performance. She doesn't need to know jack squat about the island or Dharma or smoke monster. All she needs to know is the history between Penny and Des, and the fact that Des went missing for 3 years when he swore to her that he would return within 1 year.

I suppose I can understand why it might be hard for some actors to watch the films or TV shows they're in, but the way she words it, it's like she really doesn't care. And how can you give a performance on anything if you don't know what it's about? She literally has no idea what the TV show is about at all, other than what her lines in a script tell her?
If you're acting in something and have no interest in what it is you're acting in, chances are you're only doing it for the money. It's sort of like a painter being hired by someone to paint the picture the person wants, doing it, then picking up a check once they're done, not knowing or caring what it was that they painted. It may pay the bills, but it seems hollow, uncreative and uninspired and those are the worst things to be as an actor. Disappointing indeed.

It's actually well known that most actors/actresses don't even watch their own films or TV-series becuse they tend to find things that they could've done differently or just simply feel awkward watching themselves on the screen.
"You're out of order! The whole trial is out of order! They're out of order!"
"Forget about it"

That's sad. If you take a full interest in your work, you will be a better actor.
http://learnyourdamnhomophones.com/
Learn your damn homophones.

Because she is a professional actress and her only obligation is to give her performance. For most actors, the joy of their profession comes from doing the work, not from watching it on TV.
Naveen Andrews has admitted he doesn't watch the show at all either (he's only seen the pilot).