The performer as portrait painter

Which of these images depicts Pope Innocent X? They both do. The painting is of course Diego Velazquez's portrait. The sculpture is by Alessandro Algardi. If you think "Innocent X", the Velazquez is probably the image you have in your head. Would you have known who the one on the left was if I hadn't told you? Which one is the more accurate? Does that question even make sense?

Yes, I'm still puzzling over why Calum MacDonald chided pianist Khatia Buniatishvili for what she wrote in her notes for her Liszt recital album:

'I was always aware that my first recording had to be a portrait of Liszt,' says Khatia Buniatishvili in her stupefying booklet note. 'Only he would enable me to present as a unity the many aspects of my soul.' Well, pardon my ignorance: I always thought a performer's prime duty was to convey the essence of the composer, not of themselves.

In my last post I pointed out that he was criticising her for saying something she didn't say, so the whole discussion is moot anyway. But it did get me thinking about what this means, "to convey the essence of the composer, not of themselves". What is this "essence of composer", and how can it be distilled out from "essence of performer"? Of course, if you are performing Liszt's music then it should sound like his music. But why can't it also sound like yours? Are all the great pianists great because they are ego-free and give us just the composer's intentions? If so, why don't they all sound the same? Obviously they bring themselves into the equation. Calum MacDonald complains about "the self-regarding aspects" of Buniatishvili's disc, but is it possible to be any more than vague about where the dividing line between objectivity and subjectivity should be? On the same page of the magazine, Malcolm Hayes praises Garrick Ohlsson's "objective immensity" in Busoni's version of Liszt's "Ad nos" fantasia, and again this notion of "objective" makes me uneasy.
I found this apparently anonymous sculpture online and it too depicts Pope Innocent X. The eyebrows are more obvious, the face gaunter, and I even suspect this man might have a higher-pitched voice than the two above. He's quite different from Velazquez's pope. Is this because the sculptor was more objective or less objective? It seems a pointless question, doesn't it? Are Algardi's sculpture and/or Velazquez's portrait objective? Doesn't the portrait look a bit too Velazquez-y? Surely the answer is that Velazquez's painting isn't just "a portrait of Pope Innocent X", and it isn't just "a painting by Velazquez" - it's both, and we're fine with that.
And I think a lot of the time, critics are fine with that concept too. When it suits them, that is. For instance, a quick Google search gives us a quote from an Amazon review: "Once you hear Argerich's Liszt, nothing else will sound adequate". You may nod at such a sage assessment. Or you may grumble, paraphrasing Rosalyn Tureck, "Argerich can play Liszt her way; I play it Liszt's way". Alas, I fear the notion of "objective" performances is just one of those clichéd critical rules that get dragged into play after the critic has already made up his mind about what he's heard. Until I see evidence otherwise, I shall assume "objective" is shorthand for "the way I think it should go".