It does sound like she meets the criteria for being unable to take care of herself. She most likely would here in BC. If hospitalization is what gets her treatment, that's what she needs. You're right, she's not going to get better without it. I'm so sorry. Does she trust you, do you think you could go with her to a hospital, along with the social worker? Have you contacted the NAMI affilliate in the area of California where she is? They might have some good suggestions about about how to get her treated where she lives.
I have a friend I helped when she was ill. She was paranoid too, but luckily not against me. I just said we needed to go to the hospital, in a very matter of fact way, and got my spouse to drive us there. She was confused and trusted me and perhaps realized she needed it, and went with us without resistance. That, I'm afraid is the only experience I have. It reminded me a little of trying to get a toddler to do something, where you kind of distract them from what you're doing by laying out specific choices (would you like to wear the red shirt or the blue shirt? but the option to not get dressed isn't included).
Now mostly I deal with her paranoia by offering other explanations for her perceptions.
Have you read "I'm not sick! I don't need help!" by Xavier Amador? I've heard good things about it as a source of info on how to talk to people who are too sick to know they need medical attention.
British Columbia Schizophrenia Society
A reason to hope. The means to cope.