Earlier quoted context omitted.
The claim was hundreds of picometers, which is an order of magnitude smaller than a few nanometers. Literally nothing can be perfectly flat, nor perfectly aligned.
It doesn't need to be. The basic idea is that the fly height is self-regulating; if the head goes away from the platter, its "lift" is reduced, so the springiness of the arm forces it back to the platter. If it moves closer to the platter, lift is increased, so it moves away. Similarly the tracks don't have to be perfectly round or concentric, because the lowest-level head control system in the drive actively tracks…
They have to be pretty dang close at 7200+ rpm.