No, it's like: people who point out logical errors in internet comments look more foolish - always, no matter what else they did - therefore no one who hasn’t done that looks perfectly foolish.
Or, say, people who have caught a Snorlax have more Pokemon, therefore no one who hasn't caught a Snorlax has all the Pokemon.
This assumes that there's such a thing as a "fully formed idea" (which means an exception to "always" - you can't clarify your thoughts more and more by writing about them forever). If there isn't, it's still true, but it's not saying a whole lot.
Stressing the "always" makes the argument valid only because it's a wordier version of "ideas can always be made more precise and complete, therefore no idea is perfectly precise and complete," which has nothing to do with writing. If we try to salvage the argument by making the assumption that the author obviously meant some ideas are perfect, but only written ideas, this becomes "unwrittendown ideas can always be made more precise and complete, therefore no unwrittendown idea is perfect". Which is vacuously valid in that the antecedent and consequent are identical.
The argument is either merely asserting the conclusion or invalid. I guess it's a matter of judgment which one is the charitable interpretation of the author's meaning.
Perhaps the most charitable interpretation is that the quoted bit isn't intended as an argument at all, just a restatement to cast an already-established conclusion in a different light. It's presented as a "shocking" additional implication, but perhaps it's the shock that's supposed to be novel, not the implication.
I think you're right. But I still think the quote from Graham is terrible writing: confusing, brittle, convoluted, almost as if it was designed to hide something from readers and manipulate them into a different understanding than what it actually claims.
The quote is, as you explain, technically correct due to its use of "always". Take this word away and the sentence is correct English, but the meaning now is incorrect (and would match the interpretation of the comment you replied to). Making the correctness hinge so directly in the subtlety of the presence of the quantifier makes the sentence brittle and convoluted.
It feels almost manipulative, as if the writer hopes the reader won't inspect the sentence so closely (and thus will miss this subtlety) and will understand something slightly different ("if you don't write, it's impossible to have clear thoughts"), so that the conclusion sounds much stronger. And readers do get the incorrect interpretation, as evidenced by the comment you replied to, which attacks the misunderstanding of that sentence.
So while I fully agree with you, I still think the sentence quoted is an example of terribly unhelpful and confusing writing. Especially because the full premise "writing down your ideas _always_ makes them more precise and complete" is debatable (you just need to find one counterexample).
(Incidentally, my recollection of Graham's writing is that this type of misleading sentences (that are technically correct but appear to say something else, something that isn't), as if they were deliberately cultivated.)
A much better sentence would be something like:
* "Writing down your ideas is great to make them more precise and more complete. It's hard to have fully formed ideas about a topic without writing about it." This matches the understanding of a quick glance of the sentence.
* "Writing down your ideas always makes them more precise and complete." Closer to the actual meaning, but doesn't do a slight of hand to hide the main point.
Or, say, people who have caught a Snorlax have more Pokemon, therefore no one who hasn't caught a Snorlax has all the Pokemon.
This assumes that there's such a thing as a "fully formed idea" (which means an exception to "always" - you can't clarify your thoughts more and more by writing about them forever). If there isn't, it's still true, but it's not saying a whole lot.