I gather you don't particularly care (that's essentially your point), but in case you really do want to know how it could be 1/34, and why some weirdo would insist that it does or can, I wrote up the following. :)

Is "1x smaller" equivalent to "1x larger?" If it is, then 'it's 1/33' and "2x larger/more" means the same thing as "double the size/amount." But if you have two times more than I have, then you have what I have, plus 2x that amount. So you don't have two times as much as I have. You have three times as much. "2x larger," to my ear, clearly does not mean the same thing as "2x as much." "2x larger" should mean "3x as much." That's why "33x smaller" can be read as "1 part of 34."

When we're even stricter with sense, the expression "33x smaller" becomes completely incoherent, because 1x should represent the original quantity. A 33x reduction should give us a result of -32x.

Obviously that's not what the article means. It's what the words mean, though, when you read them literally mean, rather than reading past their literal meaning to the intentions of the speaker/writer.

Most people don't care whether someone means one thing or the other, because, as you wrote, it's close enough to give the general idea.

The problem that fussy people like me and the commenter above me have is that we want people to say what they mean. And I'd wager that most of us fussy people have to do more mental work in order to get to the result that other people reach intuitively. Having to ignore literal sense in order to read someone's intended meaning is harder for us/me than it is for most people. That's our/my problem. As a matter of sociolinguistics and pragmatics, we're wrong, because literal meaning takes a back seat to idiomatic usage. (It probably does even in this comment that I'm writing.)

That's why I said these are the errors of a normal, native speaker.