Vinegar works the same way as the acid. I've used
THIS METHOD to derust some parts and it works very well and it's cheap. You just have to be very careful to rinse thoroughly. Some have suggested even using a baking soda & water rinse to neutralize any acid left in crevices where applicable.
I'm going to build a temporary pool out of 1x10's and visqueen to do my doors which are pretty much covered with surface rust that you'd never be able to grind away, nor could you get any rust hiding inside the window frame.