"Factual mistake" is a bit harsh, but the missing piece is that there are multiple ways to romanise Japanese; all of them produce "valid Romaji" but only in the particular system being used. Si is how you write し in romaji using the kunrei-shiki romanisation. In the Hepburn romanisation it's shi. See https://en.wikipedia.org/wiki/Romanization_of_Japanese#Diffe... .
Kunrei has been deprecated, Hepburn is the official one even the government of Japan recommends these days and matches better the pronunciation of the language.
But nobody cares about formal romanization rules in the first place. People have informal bastardizations of Hepburn that's consistent enough for typing, and Kunrei deprecation is more or less just admission of the status quo.
Most people use hepburn these days, it's people who learned japanese 20 years ago or so who are still stuck with kunrei.
I see, maybe my use of “romaji” is sloppy because I implied “Hepburn romaji” specifically because that’s what I chose in the article. I do explicitly mention that other romanizations exist and that I chose not to use them — so I’m not worried about misleading someone who reads the article. But on pedantic level I see why “si doesn’t exist” sounds overly broad.
I think also that anyone who's spoken Japanese for a while already has internalized that "si" === "shi" because there literally isn't the sound "si" in modern Japanese, as the other commenters mentioned it's often romanized both as "si" and "shi" in daily life, if you typed "si" into a keyboard it renders し, it goes on. The original comment on this thread includes one such person who literally didn't follow why "si" is wrong, and I felt the same way too as a long-time Japanese learner. It's a very "copy paste Western language concepts onto Japanese" way of conceptualizing the language, which is IMO a great way to set oneself up for great struggles when trying to learn a language that is structurally different, because it's not the right mental model.
I’d normally be with you and I call this out as a concern purists would have my article. I’m doing something differently here and maybe more daring — the conceit of this article is that you can learn the entire system in one evening with no prior knowledge of Japanese at all. In that case I think the “s_ + i = shi” is as fine a pedagogical moment as any to introduce why the hiragana table matters. And for readers who already know it, I assume they won’t actually have a problem following the content, setting aside the pedantism and the annoyance at someone seemingly “teaching in English” and “copypasting concepts”. Like I get what you’re saying, I just think that it’s okay to break the rules for what I’m going for here.