The main melody notes are displayed if they are also on the "Navigate Channels". For my CTK-5000 this defaults to channels 3 and 4 (or is that 4 and 5?) when first powered-on. If a song is not displaying the notes, I use the keyboard's MIDI options to set the "Navigate Channels" to those channels that the melody notes are on. Typically this is channel(s) 1, 2, or 3 in public-domain MIDI files.
If you open up a MIDI file in a MIDI editor and look at the notes being played on the various channels (of 16) you'll see how you can select the notes from different instruments in a MIDI file to be displayed on the keyboard, just by selecting a new pair of "Navigate Channels". The left and right hand displays (for lessons) are coming from two adjacent channels. This is also a good way to create your own lessons for left and right hands, by using a MIDI editor and putting the respective parts on two adjacent channels. Left-hand lower numbered channel, right-hand higher numbered channel.
I used a program like Cakewalk (or something similar) about a year ago to do this. It allowed me to select all notes in a song below a certain note and then copy them over to a new track/channel to separate out the left-hand part (mostly). Just to see how it was done. As far as which MIDI track/channel the actual fingering number is recorded on for lessons, I never bothered to investigate that. But I assume it could be deduced by playing back a lesson with MIDI out + accompaniment turned on, and recording that lesson in a MIDI editor on the PC, then looking at the tracks to see which contain such simple commands. It might also require triggering a unique "tone" number and bank number to trigger it from an external MIDI input source. That is beyond my investigative abilities.
(Lightbulb goes off. For full song lessons with fingering included: The human-emulated voice-numbers are on the topmost/highest 5 keys of the keyboard (Gb-C) when you select any percussion tone-set. These could be recorded in any MIDI file. Though I don't know what track/channel they'd have to be on to get them to display visually instead of aurally. It might also be something as simple as the next 5 notes above those (beyond the keyboard's range) trigger the finger-number display. Because when I raise the octave of the keyboard, no instruments/tones are assigned to those notes at all. Interestingly, there are more percussion instruments above that blank spot and it doesn't seem to be wrapping around either. Cool, more undocumented features?!)
You might also want to check into a program called "Synthesia" as a simple way to learn songs from MIDI files, using your keyboard as the input/output device.