This is btw another proof why this is not the real color/number correspondence: that's only the deafult palette, you can change it to whatever you like
VGA cards use it as the default for backward compatibility. It was introduced by CGA cards, and on those it was not merely the default and could not be changed; it was hardwired. (CGA cards did not have any way to display a color given arbitrary red/green/blue values. They *only* had the sixteen colors, ever, period. As an added bonus, you could only get more than four of them on the screen at once in text mode (although there were tricks available to make text mode appear to be a low-res graphics mode).)
I was pretty sure the CGA colors also match the ANSI colors, but I shouldn't be surprised that the VT100 used a different scheme; DEC did a lot of things differently from the rest of the world, such as using Category 4 (not 3, not 5) cable and MMJ connectors for networking, or the extraordinarily wacky way VMS expresses directory paths.