In addition to what you write, is not the negative in negative feedback, simple because it is subtracted?
If I get your meaning, probably not. In most amplifiers the feedback is applied to a node that has non-linearities, so often feedback signal itself contains distortion not present at the output! For example in a typical solid state amp, the input circuit is a differential amplifier. One of its inputs (differential amplifiers have two, one inverted and the other non-inverted) takes the signal. The other takes the feedback. But the device (transistor) isn't perfectly linear... Of course, if you applied enough feedback, you could overcome this issue...