You are right, the PAPI is deliberately misplaced, the rest is geometry.
An old topic albeit not discussed frequently, explanation blends into landing performance a bit.
Firstly, the stable approach criteria include landing within the first 900 mtrs or 1/3 runway, this causes much trouble so forget it. The correct landing point is the one calculated from following the profile to 50' over THR, around 450 to 600 mtrs past THR.
The 50' datum and 3° profile create a geometrical aiming point. For my airplane the flight-path (GS) ground intercept point is located 298 mtrs past the threshold. Because the antenna is pretty much same height as the pilot-eye position, the visual aiming point is right there.
Picture:
Green spot = 3° path intercept point
Yellow dot = where the plane is actually going (check g/s dev and v/s, the flare has started
Red line = PAPI distance line aligned with the "aiming point" markers as per ICAO standard for RWYs longer than 2400 mtrs.