That’s a coincidence, I was learning to play Billy Jean earlier in the week just for a bit of fun.
This guy explains it really well and definitely hit on about a synth playing the added octave.
I like the version two starting on the second fret of the E string, that’s the version I learnt, it’s a pig of a song due to the repetitive nature of it, you cannot afford to fall out of time, otherwise it falls apart.