Violet, Indigo and Red are different hues. Pink is not "light red". No adjustment of the saturation of red will ever make it pink. Brown is created with a low saturation of red, orange, yellow or green.
That is a purely semantic argument. It's also a contradictory one. That article says in the first sentence that they are considering adjusted hues as "shades" or "tints" of red. Using terminology beyond HSV only introduces semantic complexities to confuse the topic.
Wikipedia is a terrible source for this type of thing.
“Pink” was until recently a synonym for “light red”.
However, when it became possible and fashionable to produce more bright purple-red colors, these were also called “pink” (“hot pink”, etc.) by marketers, and now our late 20th/early 21st century concept of the denotation of the word “pink” is considerably broader than 50+ years ago.
You can't adjust the saturation of that color to make it red, just a lighter shade of pink. There are pink colors that are closer to red than to purple, but pink is a different part of the color space than red is.
If you see the shade in that link as red or purple, then you're living in a hell of having no rational basis by which to talk about color, or possibly color-blind.
Up until the last few decades, English speakers would not consider the color in your link to be “pink”. “Pink” was another word for “light red” (not the name of a hue), named after a flower that looks something like https://www.stauden-stade.de/img/artikel/full/823.jpg
“Hot pink” is a creation of the fashion industry / marketers from the 1980s (or maybe 70s?).
If you want to be unambiguous, you should call the hue of your link purplish red or similar. You could also use a word like fuchsia (named after a different flower) or magenta (a purplish red ink used in 4-color CMYK printing).
