'Fanned fret' is a copyrighted term, I believe. Ralph Novax 'invented' multi-scale fretting some time ago, and actually got patent on it. Then it was pointed out that the concept goes back to Orpharions in the 17th century or maybe even earlier. The patent was thus invalid, but I think he still holds the copyright to the term. Hence it's often referred to as 'multi-scale'.
There are a number of reasons cited for using it, but better intonation is generally low on the list. It's difficult to get decent intonation on a too-short string, of course, but normal guitar sets for six-string instruments are correctly sized to minimize that. If you extend the scale down with extra strings, and/or use a particularly short scale, you might run into problems. I've made multi-scale guitars with steel strings, which have more intonation issues than nylon. I don't think it makes a dramatic difference in intonation or even tone for the most part.
Keep in mind that it's easier to get all the frets in just the right places when they're parallel; fanning them out introduces some uncertainty, unless you're cutting them with a computer controlled milling machine or really precisely made jig. It might be hard to gain more precision in intonation than you lose.