On non-precision approaches one can see big differences between the PAPI angle and the vertical descent angle. E.g., at Greenwood Lake Airport (4N1)
RNAV (GPS) RWY 6, the descent angle is 3.15 degrees/TCH 40 but the PAPI is at a very steep 5.75 degrees/TCH 39.
The FAA Order 8260-19,
Flight Procedures and Airspace, gives this guidance: "n. VGSI and IAP glide path angles/vertical descent angles should be coincidental (angles within 0.2 degrees and TCH values within 3ft)." Otherwise the difference must be charted.
In reality, it's quite common for the PAPI and the ILS to be non-coincident; that's not a problem in itself.
As McNugget mentions, PAPI designers must consider different eye-to-wheel heights. A 747 might have an eye-height of 45 ft, while on a 737 the eye-height is around 20 ft. Thus a PAPI will be "more coincident" for some aircraft than others.
At large airports, they will put the PAPI further down the runway to accommodate the 747s. If you use the PAPI on a Dash-8 (11 ft eye-height) to the flare, then you will land on the long side.
The possible issue is when two pilots of a crew use different references (PAPI vs GS) and the plane's eye-height is very different from the design eye-height. Plus in the case of this crash, the cues provided by the HUD might be of a further factor.
In Canada at least, you can find out the design eye-height for a PAPI in the charts (coded as P1, P2 and P3). The design heights are: P1, <= 10ft. P2, <= 25ft. P3, <= 45ft.