"But it still doesn't alter what I said about fixed pitch and non-fixed pitch instruments."

No it doesn't, nor what I said about being accompanied by fixed pitch instruments. The chart illustrates the differences though, and they would be detectable by modern electronic tuners or an oscilloscope. To be honest, I think by the time a non-fixed pitch player had finished applying the bit of vibrato which (arguably) brings such instruments to life, the difference is largely academic - though that doesn't universally apply, obviously.