Myth 1

Without thinking you carelessly say "the frets does not note true". This fault is rare on modern instruments, but the expression remains and leads you astray. More about this here.

Just temperament versus equal temperament

It is a very common belief that we must accept that guitars and other fretted instruments have to sound out of tune because they are tuned to equal temperament. There are endless discussions about just temperament versus equal temperament. These discussions does not belong here. Off course fretted instruments should be tuned to equal temperament - the mathematical formula for calculating the fretboard is by definition equal temperament and all electronic tuners will tune to equal temperament. It is the flaws in intonation of the fretted instruments that makes it impossible to even get close to equal temperament.

Inharmonicity

Inharmonicity is another source of confusion. Inharmonicity is caused by the fastening faults in the nut and bridge and makes the overtones in the string pitch too high. The fastening faults are corrected by the intonation, but the inharmonicity in the string remains. In pianos the tuning is stretched because of the inharmonicity - not to improve the tuning but to increase the sustain (better resonance). Inharmonicity does not exist on wind instruments. Unless you don't play a lot with a piano there is no reason to stretch the tuning of fretted instruments.

Myth 2

Inharmonicity is also the cause for the misconception that old strings intonate worse than new strings - while in reality it is exactly the opposite! How can you find the right solution if things you take for granted is wrong? More about this here.

Different tuning methods

Many different ways of tuning fretted instruments are devised. These are simply different attempts to spread the faults so they won't be noticed so much. The faults does not disappear, they are only moved to different places. If an instrument is intonated to equal temperament, any tuning method will work! The only rule is that only octaves and unisons should be tuned pure (without beats). Don't tune any other intervals pure.

If harmonics are used for tuning, you should be aware that they, due to inharmonicity, are a tiny bit too high. You get an uncontrolled stretching of the tuning, different on each string.

Guesswork

Finally it seem that nobody has analyzed the errors properly. There are a few other intonation methods on the market. They all have in common that the distance between the nut and the first fret is shortened, but the rest of the methods are pure guesswork. You can never achieve perfect result with generic methods.