Thank you Guv1976! The thread is very helpful, much more than any other sites out there. I just cannot call up my cc's rep and ask. They're clueless.
I'm getting a much better understanding now. So my home insurance will not cover liability, and according to the thread, no credit card will.
So, I think the most logical way of insuring myself w/o wasting money, is to just decline LDW, use cc's coverage for the car, buy SLI to cover liability, and buy personal accident for bodily damages.
Thank you everyone.