That's a fair question, and I'd also ask what you meant by corporations "providing for our health."
Personally, I would expect that I'd probably have insurance for something unexpected like this. Or perhaps I'd simply keep a certain amount of cash on hand for unexpected medical issues, and use that to pay a doctor to set the broken arm, put on a cast, etc.
I would actually trust corporations a lot more than I would the government. In theory (if they haven't colluded with the government) the corporation actually has an incentive to satisfy my needs (I'm assuming we're talking about an insurance company). Of course, there are mitigating factors, like how much competition there is for my business, but it's gotta be better than a government monopoly (unless it's an actual private monopoly colluding with the government or something, at which point it's probably about the same).
Maximizing profit while satisfying consumers is generally a good thing. For a health care related example, take a look at the corrective eye surgery industry. The procedure is generally not covered by insurance, so there is competition both on quality and price.