While there are some people who are either scared of those who push the boundaries or see terr'ist potential in everything, there is a common belief among the real amateur rocketry community (i.e. Armadillo Aerospace, XCOR, etc.) that a rocket, guided or not, is simply a transportation system. A missile indeed implies an engine (jet or rocket, guided or unguided) plus a warhead.
Reverend's hypothetical device is an actively guided rocket. Rockets with just fins are passively stabilized. (Active stabilized vs. active guided is a matter of semantics and context.)
Other examples:
Saturn V: actively guided rocket, no warhead, not a missile.
Tomahawk: actively guided missile (rocket booster, turbofan cruise), has a warhead
During and after WWII there were also unguided missiles.