Well, in various philosophical traditions the observer can be hypothetical so that he can observe things that otherwise wouldn't be directly observable, such as an Einsteinian "observer" that can right light waves. What they mean in most cases is that there just has to be something to observe. But you're onto something. Buddha's scenarios are carefully contrived to have the exact mix of hypothetical allowances and practical limitations to make his proof seem like it works. Hypothetically speaking, the evidence showing the origin of the universe is set to be analogous to a videotape, limited in other words to sequential playback and subject speed but magically capacious enough to hold all the evidence. Then the punchline of his proof is that such a volume of evidence would be too much for the human observer to review in a lifetime. Now all of a sudden the human observer's limitations become important. The modeling and encapsulation of the evidence can be as hypothetical as it needs to be, but the observer modeled to be able to digest it in the contrived form suddenly has limitations, and those limitations -- i.e., properties of the model, not of the thing being modeled -- are what his proof hangs on. So yes, he's begging the question in a sense, because he's built his thought experiment to have exactly the properties it needs in order to make his proof come out the way he wants.
In the immortality thread Jabba tried to hide his begged questions in math he hoped no one would understand well enough to refute him. Buddha is hiding his begged questions in esoteric philosophy he hopes no one understands well enough to refute him. That's I think why he's clinging so desperately to the gaslighting ploy of making sure his critics know he's so much smarter and better read that they, and that he doesn't have time to go into as much depth as they have.
Now if I remember correctly, in some prototypical forms of positivism the observer was literally limited to the human senses. But for obvious reasons that doesn't lead to a model of knowledge that has much use outside of coffeehouse musings. It's why I asked whether it would take 50 years to prove someone's claim to be 50 years old. In the least useful philosophical models that's what would have to happen. The only way someone could prove he's 50 years old is to cause his entire lifespan to be continuously observed from his birth. In that model, it would be impossible for someone who's only 30 years old to know -- the way these models define knowledge -- that anyone was 50 years old. It would then have to use some sort of testimonial or propositional evidence, which strict positivists reject as a basis for knowledge. This may be what Buddha means when he says not everyone will accept his proof. We would reject it because it relies on the all-too-apparent limitations of the dark dusty corners of some brands of philosophy. And why he correctly notes that some later philosophers have rejected them. To accept such a philosophy to its furthest extent would have to conclude that all modern science is incapable of knowing anything, which is sometimes what claimants at ISF are trying to prove.
And the notion that a proposition is false if it that cannot be verified according to those limitations falls pretty flat. The truth value of the propositions are what those philosophies seek as a matter of knowledge. When knowledge is modeled as only what can be verified by some empiricism, asserting the falsity of an empirically unverifiable proposition is an error. They correctly say that the truth value of such propositions cannot be known -- in effect that the propositions should be regarded meaningless as knowledge. This is what Phiwum and others were trying to get Buddha to see as a contradiction in his proof. The effect of empiricism varies in his proof depending on what role he needs to to play so that it comes out right.
And in the broadest sense this makes Buddha's proof fall into the standard pattern of fringe claimants. They want to prove something they know they can't prove directly. So they try to prove it indirectly by deducing what "must" (or can) hold if the prevailing narrative cannot hold. Then they propose to refute the prevailing narrative by one contrived method and standard of proof, making sure not to hold their desired conclusion to the same standard. A different standard, if any, is proposed instead. Buddha contrives a method to disprove competing explanations for the origin of the universe, but then when we try to hold his deduced finding -- a created universe -- to the same standard, he handwaves it away with some pseudo-philosophy mumbo jumbo he insists his critics aren't smart enough to understand. Then he says "further" proofs are necessary, tailored only to that conclusion.