There are a lot of techs who do not fully understand MIDI. In addition, MIDI implementation varies from mfr-to-mfr. MIDI implementation refers to what MIDI functions the unit can transmit and receive.
In order to troubleshoot a MIDI 'problem" (most are really user error), you need to know that MIDI implementation of both units in question here. You are definitely receiving MIDI "note on/off" information, but since only one patch is usable, you need to find out more about patch-change information, i.e how it is handled by the FP-4 and also by the controller in question. "Local Control ON/OFF" is like virtually (dis)connecting MIDI from the internal keyboard to the internal sound engine.
Usually, this info can be found in an Owners Manual.