I think, I would call road service before, I ever use a factory jack.
My LeSabre scissor stock jack actually bowed and dropped the car, so I can understand where you're coming from. Also, the rod for it had a socket on the end for the lug nuts, and instead of being welded perpendicular to the rod (like any jack should be),it was free to pivot, which means that it takes more work to get the stupid nuts off, and more importantly, that nuts will round off and break...as I found out the hard way.
That said, I've used my ST jack several times to lift the front...with jackstands immediately inserted, since I don't trust the head of the floor jack to stay on that curved piece of metal on the frame for jacking, same with my bottle jack...a flat head against a curved piece of metal just sounds bad IMO.
Though the stock jack is WAY too short, several times I've had to put the jack onto cement blocks (solid, like the ones a patio could be made from, not cinder) to get the jack high enough so that it could actually
reach the jack point. It needs some viagra something fierce.