Patriots don't go very high. A Patriot interceptor is only going to knock the missile down only if it actually descends down on Japan.
If you want to hit a NorK missle that is at higher altitudes you either need THAAD or an Aegis-guided SM-3.
More info here on this video.
Pic of SM-3 at liftoff.
I believe their concern is IF the NK booster fails and there's a risk the vehicle may come down short on Japanese territory. In that case, Patriot could be used to break up the vehicle and disperse fuel/oxidizer high enough to reduce risk to civilians.
A lot of "ifs", "ands", or "buts", I know. But considering the explosive power contained in a fully-fueled rocket stage and the failure rates associated with booster development, perhaps a not-unwarrented concern.