As pointed out in the video you posted, many instruments are tuned with some compromise built in for various reasons. The reason for tuning to a frequency other than A=440 can be different depending on the instrument.
Harmonica's are tuned to a specific key unlike a piano which is tuned so that it can be played in any key. The reason some harmonica players may prefer a slightly sharp tuning, is to compensate for their particular playing style. Those who blow more forcefully tend to create a different vibration pattern in the reeds which can cause the intended pitch to sound lower. So they compensate by using a harmonica tuned slightly sharp.
Many guitarists are joining a growing trend towards tuning their guitar to A=432 Hz instead of the standard A=440. Guitarist who choose to alter their tuning frequency from the standard A=440 Hz, often do so because they feel that it will sound better, or more pleasing or will be more harmonious with the natural vibration of the universe.
One problem with a guitarist choosing a non-standard tuning frequency, is that if he/she plays with instruments such as a piano or harmonica, the guitar will sound out of tune. So if the guitarist plans to play with other musicians, all instruments must be tuned to the same frequency.
Here is an article online that very thoroughly explains some of the theory behind the A=432 movement among guitarist. A-432 Guitar Tuning Theory
There are many other articles about this on line.