The woman from Michigan received a citation, I believe, for violating carseat laws. As I recall, that was it. There was a huge thread about this here, but I can't remember if it was in breastfeeding or TAO; maybe both.
When I pull off the road to nurse, if I'm driving I get back into the driver's seat and pull it all the way back and down. If Mike is driving, I do it in the front passenger seat which is always all the way back and down. Airbags can, on rare occasion, deploy for no reason at all. My impression is that it's more likely to happen in older vehicles, but you can't be 100% certain about anything so be as safe as possible. Our vehicle is relatively new, so I don't worry about it too much. I feel much safer pulling off into a parking lot to nurse than I would if I kept driving while we nursed.
And yes, if the weather permits it, I turn the car off; if it's really hot or humid, though, I don't.