No the source is the signal. If want to recreate what the sound engineer heard you'll need that information and to use the same gear in the same situation. Otherwise you are just muddying waters to no benefit to anyone.
You've misunderstood what I said. Specifically in terms of amps, yes the signal that their output should be faithful to in everything but total level is the input source signal (and as I've said, this should be fidelity to a music input signal, as transparent fidelity to sine tone input does not necessarily guarantee the same for music signals.)
My second point in brackets in my original comment was that specifically for transducers used for audio reproduction, they cannot be said to be faithful to anything but an acoustic 'signal', as they are analogue audio to acoustic converters. So this acoustic output signal of the transducer should ideally be faithful to the acoustic output that the sound engineer heard when listening to the final master of the music, in order to preserve the intent of the artist.
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