What PG is saying is that if something is ugly, you can conclude that it's most likely wrong as well.
Attention to detail is a signal of quality, but these things are just heuristics, not reliable truths.
The article says it is ruling out both of these possibilities, as other posts elsewhere in this discussion have already pointed out.
I don't see how. Your post was disputing the claim that good design, craftsmanship, beauty, etc. are signs of correctness. And that's not the claim PG makes in the article. Your post never disputed the claim PG did make, which is that bad design and craftsmanship, ugliness, etc., are signs of lack of correctness.
The essay itself lacks anything novel, despite the rather breathless framing: “So here we have the most exciting kind of idea: one that seems both preposterous and true.” These ideas are a couple of hundred years old at least. Kant: “the beautiful is the symbol of the morally good”. This is classic Age of Enlightenment stuff, repackaged in classic Silicon Valley VC style.
but the best communication survives too because it touches universal truths by connecting them with specific real phenomena. the worst (most harmful) communication survives because it frantically goodharts our quality evaluation process, even when it contradicts truth or reality. e.g. Orwell on the good side, L Ron Hubbard on the bad side. Unfortunately these categories are often not well sorted until after the principals are all dead (probably because everyone has to die before you can tell whether the values are universal or just generationally interesting), and there's a style-bar that has to be cleared before you even get to join the canon for consideration; interestingly this this would tend to increase the illusion that style is associated with substance, especially in older writing.
But towards the end he backs away from that claim, and makes the claim I described:
"[W]hile we can't safely conclude that beautiful writing is true, it's usually safe to conclude the converse: something that seems clumsily written will usually have gotten the ideas wrong too."
In the light of that, and of much of the rest of the essay, I think the sentence from the start that you quote was misstated. It should have been stated as "Writing that's right is likely to sound good."