IanS, you are doing exactly this:
Even if you presented rock solid proof a real BIV is impossible, it will not change the argument/point.
The argument/point is theoretical.
There is NO real BIV in a thought experiment.
I have no idea what you are now talking about, and in the words of Sam Harris "what's more, I don't think you have either!"

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The so-called "BIV" argument of philosophy, is a word-argument; an argument about, and from, a construction in the selective use of language. That point is actually inadvertantly highlighted in that linked article (note how many times it has to talk about it's semantic nature and about what should be, or should not be, the meaning of the words that the argument prefers to use. It is also an argument that even within philosophy itself, has been shown to be if not actually flat-out wrong, then at least in serious doubt ... but far worse than any of that ...
... it is also an argument that has to begin with various unwarranted un-evidenced assumptions of the most fanciful kind, which in your language here, you tried to justify by avoiding the word "assumption" and saying instead it is "a given" ... well that's just yet another selective use of language in attempt to hide the fact that you are making assumptions, such as the assumption that a BIV (if that were even possible at all, and you certainly cannot show that it is) would experience the identical things that a human brain experiences in a real world body with real world surroundings ... when you write things like "that is a given", that is just a form of words used to obscure/hide the very obvious fact that it's actually an assumption on your part.
But apart from all those problems with the philosophical word-game known as "BIV", that entire scenario of a BIV is not in any case an example for solipsism (which is what you were presenting it as). In the "BIV" it is necessary to have an external reality in the first place. Whereas in solipsism (as insisted upon here by Larry, and then supported by yourself and David Mo) there can be no external reality.
If you want to believe that claims such as “BIV” or Solipsism might be true, then your very next thought ought to be the realisation that absolutely anything “might” be true! It might be true that the person who thinks they are an alien who has created a brain in Vat, is himself just experiencing an illusion in his own mind, so that he is not actually an alien, but just a deluded human (eg a deluded human philosopher), who does not have any BIV, but who is instead just dreaming, hallucinating, or otherwise mentally inventing ideas that are taken from what is his actual real experience of real people, real brains, a sense of our real surroundings, a real exposure to alien stories in books etc., ... that are in fact all real parts of his own real world experience and his own real existence.