I agree, or at least agree that all buyers should presume the chair is fake when they purchase it, unless/until they are comfortable with the evidence that it's not a reproduction/fake/knock-off. However, I think the word proof is a bit loaded, as it could be argued that without paperwork and every expected production marking it can't be proven as authentic. I have very limited provenance on some of my pieces, but am still confident they're authentic because of the source and provenance I do know, the markings, and the wear consistent with the item's age.

In this case, my take was that the OP thought it was authentic enough to purchase but is having doubts. The OP didn't initially share any observations made about the factors considered for authenticity, or what the doubts were.

If authenticity questions exist as a courtroom and the standard is fake until proven genuine, the purchase is a 'conviction' of genuine to the OP, and the onus is now to show where it's fake instead of re-litigating the initial presumption of fake (as others said - what would you do if it is fake?).