Radiator hose burst

As far as causing white smoke, yes, it could cause white smoke/steam. As far as the inspection goes, it might have looked fine during the inspection 4,000 miles ago. Was the car overheating when it happened?

This is one of the issues with the hoses and belts used on modern vehicles. They can visually look 100% perfect, and fail the next day. Just the environment they are used in works to cause them to fail, high heat, constant flexing from engine motion plus the chemicals in the air and in the hoses, it is amazing they last as long as they do.
I have removed hoses that looked great from the outside, that you could push your finger through because of internal damage. It is the reason why I replace all belts and hoses (except AC and fuel lines normally) when I buy any vehicle with over 50,000 miles on it. The money spent to flush the cooling system, install a new thermostat and replace those parts is a lot cheaper than the engine damage that can happen if they fail.