The raw words written to the drive are actually re-encoded into slightly larger codewords with nice properties like not having too many zero or one bits in a row, and error detection/correction.
Plus I think that the 0/1 bits are not encoded as "no magnetism"/"some magnetism", but instead as "north magnetism"/"south magnetism" since magnetic fields have a direction.
And I don't think the magnetic fields on the platters have any appreciable effect on the head besides the electromagnetic effects at the sensor.
Essentially the same problem as with fiber optics. The data can't be recovered unless there are frequent bit transitions. In that case the data is transformed to ensure illegal patterns cannot occur.
