They're going to have to use heat - specifically a heat gun or hot air desolder station (same thing, really) - to get the BGA off in the first place to reball it, but if it's done properly it's perfectly safe. Generally the entire board has to be heated up (not enough to flow solder, though, but enough so that the board won't flex when the component to be desoldered is heated up), then a heat reflective shield is placed around the component to be desoldered (to protect all other components), a heat gun is used to heat just that component up enough to get the solder flowing and then a vacuum cup thing is used to lift it off. Then the reballing happens and the process is repeated in reverse. There's no way to remove a BGA without heat though, and no way to reball a BGA without removing it.
