This brings us to a different but equally interesting topic: how can classicists be sure of this (or any) fragment’s authenticity without the information about the papyrus?
Ultimately they cannot, but it is important to remember that there are other things besides the physical carrier: language, meter, poetics, biographical data… Some could even say that textual criticism was brought to life precisely by the need to expose forged texts (think Lorenzo Valla and Constantine’s Donation), the task that people like Joseph Scaliger or Casaubon handled with such a mastery. Note that much of this development took place before papyri entered the scene (with the excavation of Herculaneum in 1752, and the publication of the first Greek papyrus in 1787). Basically, over past centuries Classical philology has accumulated a lot of experience and knowledge struggling with questions of text authenticity. It’s not just about the object: we are able to evaluate the text. (In particular, sometimes people even talk about an authentic text transmitted on an unauthentic object, think of the Fibula of Praeneste).
So is there a possibility that our text is a fake and the discussion is, as Prof. Walsh suggests, premature? This suggestion, I think, can be evaluated and others are invited to contribute. The starting assumption, I believe, will be that Dr Obbink is not a Thomas Wise and would not risk his reputation in order to pull a prank on the scholarly world (as was Wise’s intention, at least according to Bernard Shaw). Prof. Walsh may disagree, but on the one hand, the amount of important contributions Dr Obbink has already made in his career would satisfy any scholar’s thirst for fame, and on the other hand, in the digital age the risk of being exposed is much higher than it used to be.
I therefore think that under the hypothesis that the text is unauthentic one would need to assume that Dr Obbink was misled by an unknown villain, who managed to 1) prepare ink and prepare (or obtain) a sheet of papyrus, 2) imitate the script, and 3) mutilate the papyrus. None of this is impossible, although this would have been a remarkable feat.
But the villain would also have to have composed the poem in impeccable Aeolic dialect and meter, and — this is very important, to me at least, — his or her command of Sappho’s Lesbian does not seem to be entirely derivable from the existing handbooks and descriptions: the poem seems to contain several forms that have not been previously attested in the corpus of the Lesbian poets or in the epichoric Lesbian dialect.
This brings us to following: if this text is a fake, the forger must have been an outstanding papyrologist with vast knowledge of papyri- and ink-preparation technology; a brilliant paleographer; his or her knowledge of Greek dialectology must be staggering; and of course the villain in question would have to be second to few as far as their expertise in the corpus of Lesbian poets is concerned. One or two possible candidates may exist, but in general it seems to me that the chance that the text is a fake is rather negligent, which is why the classical philologists may discuss the text, however provisional these discussions may be. I hope I answered at least some of your question.