Why do most of us including many singers sing out of tune and below ie flat rather than sharp?

One important explanation seems to be on the begining of chapter :The Influence of Mind, on the fabulous book Sound and Hearing - Stevens, Warshofsky created after so my experiment at the Harvard university's Psycho-Acoustics lab. At high sound intensity the brain hears the same frequency flater ie with lower pitch. So the singer thinks she, he is singing correctly in tune, but in fact everything is below in frequency by a little but very annoying amount. And this may make a potentialy hit song not a hit song at all. What do the Whitney Houston level singers do? Do they sing on purpose higher so that the mistake sounds correct? Do they get a very low volume output to their headphones so that their brain hears the correct pitch on the backing track? Do they have immunity to the pitch change by highter intensity? Do they get their voice loud enough on their headphones so that it sounds flat too as well as the backing track, and the producer fiddles with the mix until intonation is correct? Phil Ramonne on his book Making Records states clearly that whenever a problem of intonation by the singer is encountered the first thing to take care is the headphone mix... Also Sir George Martin states in his All you Need is Ears (if memory is correct) book that good singers when they say sing just a note on their own the result sounds in tune with itself, meaning (if memory is correct on reading the book) that the overtones of their voice sound in tune with the fundamantal to the listener's brain...