I’ve lived in Australia my whole life, never been to Canada, etc - and yet I immediately assumed “B.C” meant “British Columbia”. It just seemed like the most likely expansion in the context (looks like a news headline, posted on a North American website). Although a bit like you, my initial parse of the sentence was that she was crushed to death in a warehouse accident, it took me a couple of seconds to realise it was more likely meant figuratively
It is true that Australians and Canadians find themselves to have certain things in common, both being former dominions of the British Empire – but that doesn't mean that Canadian provinces have particularly strong salience for Australians.
Australians consume a lot more American media than Canadian media; and the US is a significantly more popular travel destination. I have a much better idea of the difference between New York and Florida than the difference between British Columbia and Ontario – I've been to both New York and Florida, as I said I still haven't got around to visiting Canada; even before I'd ever been to either, I'd watched countless TV shows and movies set in both, and that gave me a certain image of both in my head (and actually experiencing them in person wasn't hugely different from my pre-existing mental image). I think of Canadian provinces, and my mental images are a lot vaguer. I think that's generally true – the average Australian, if their idea of US geography is somewhat patchy, their idea of Canadian geography is likely to be a lot patchier.
I don’t expect that Australians hold a bond with Canada at large, I can’t very well imagine any of the Aussies I’ve met having a fond place in their hearts for Calgary or even the rest of Canada (read: Toronto, Montreal).
Now I think about it, years ago, I did hear something about Australians working in the Canadian ski industry, and I suppose that probably was in BC. But I've never really been into skiing, so the information didn't make much of an impression on me. So I doubt that's got anything to do with my immediate understanding of "B.C. woman..." as being a reference to British Columbia.
Also, one of my aunts (by marriage) is Canadian, and if I remember right she grew up in BC. But I've never been particularly close to her, and I haven't seen or spoken to her in years. So I'm sceptical that has anything to do with it either.
I'd say also that B.C people are fairly likely to want to pursue visiting Australia, despite not really digesting any substantial amount of Aussie media.