I'm not "having so much trouble understanding it", it's just that publicly subsidized insurance is ... subsidized. It's not a complicated or "semantic" question. You've created this other definition of what "subsidy" is, which just isn't what it is. If the government subsidizes something, it's a subsidy.

I don't get why you're so attached to doing contortions to deny that. It kind of seems like you think subsidies are good things, but that this subsidized insurance is bad, so thus it can't be a subsidy. But it's easy to square this circle: sometimes subsidies are good but often they aren't.

To your last paragraph, I think you just aren't aware how much other states are also struggling with this problem. You seem to live in California, so it's understandable to be most aware of what's going on in your own state.