I am very familiar with the target parameters and methodology used to calculate (estimate) missile range for air targets.
I believe 120km is way way low.
I am not familiar with the parameters used to calculate range for ballistic targets.
My guess is that the target that the ballistic missile is attempting to destroy must be located within 60km of the Patriot launcher.
Also, it is counter intuitive that hit-to-kill is more effective than blast-fragmentation.
My guess here is that proximity fuses can't handle the high closure speeds.
Here’s a document from LM that pitches the HTK advantages over blast frag.