Correct although this does not answer why the flywheel will not go down without the key. There is no reason to "Crank Down" a flywheel. It should drop right on and seat. Check for a loose, dislodged magnet in the flywheel. I would also point out that a B&S key is ONLY to correctly position the flywheel to crankshaft until the flywheel nut/bolt is "properly" torqued. It is not to keep the flywheel from turning.
Walt Conner