in other words, taking advantage of LSI means using synonyms in your body text and in your links too. (also note that my comment says “PROBABLY” but I still believe it)

To rewrite your “understanding of the premise” I’d say this -
If I want to rank on a phrase that I don’t have on my page all I have to do is put LOTS OF RELEVANT CONTENT WITH SYNONYMS AND links containing SYNONYMS of the phrase to OTHER PAGES that MAY (probably should) contain the phrase.

In my opinion, the search engines use of LSI is not something you can “rely on” solely for ranking, but rather should be considered a byproduct reward of having a well written, well structured, and well crafted website.

Let me see if I understand the LSI (Latent Semantic Indexing) premise. If I want to rank on a phrase that I don’t have on my page all I have to do is put a link containing the phrase to another page that does not contain the phrase anywhere either.

I guess this really does change the way SEO is done. Are we going back to the days of stuffing keywords?

True, the number one listing for antique tub does not contain the word antique in the title tag, nor description or H1 tag either.

I do see the body of the landing page does contain a link – “Antique Clawfoot Tub” right above the footer, and it is pointing back at the home page.

So how to explain your example above, for the number one ranking does not use the phrase in the title tag, or feature it prominently on the page, or even have an inbound link with that exact link text?

In my opinion, the example you are citing above is probably a perfect demonstration of LSI – (Latent Semantic Indexing) working exactly the way it is supposed to. That is, based on all of the other phrases and text used on that page, Google has determined relevancy based on synonyms and content.

For years people have been saying LSI would change the way SEO is done, and I can’t think of another explanation…