The portion in bold is correct.Because Hawk Eye seems to map the flight path only in 2d, I don't think the animation is meant to show the actual path. Such an animation is nicer to look at than a picture saying in or out.
The Hawk-Eye system being used for badminton is a 'lite' version.
It is not the feature-rich full version that tennis and cricket uses.
The animation we are seeing now is a pre-set sequence.
Even if the shuttle drops straight down or hits the floor at a very acute angle, what we're going to see is the same animation of the shuttle approaching (and exiting).
Right now, the only calculated-and-mapped element in that sequence is the landing-spot (the end-point).
The system has errors (but you won't hear this from an official mouth)

For now, let's say the errors have much to do with these factors:
- sudden peaks in lighting when the shuttle flips 180 degrees after being hit and during the shuttle's flight (the white, shiny feathers make this worse) which 'blind' the camera sensors
- players blocking more than one camera's view of the shuttle (this is very pronounced during doubles matches)
In cricket, the path (of the ball) to be tracked is always in one well-defined area (in front of, over, behind and on the stumps) and always in one direction - from the bowler to the stumps.
In tennis, the defined area is much bigger (and so is the system being used) but the ball does not 'burn' in the light, does not reflect highlights and is easily trackable especially because it almost never gets blocked by a moving player.
Nevertheless, what is immensely worrying is something else.
In live tests, it's clear that the landing spot predicted by the system is not always true to the actual landing spot (as shown by simultaneous video monitoring). And it's not a 5mm error either - it's much much larger than that.
Unless the BWF decides to use a full suite, the Hawk-Eye system will continue to be much less reliable than honest human eyes backed up by slow-motion video replays!