Are human beings, even singers, flat by nature?

We know from the first paragraph of the chapter Influence of the Mind on the great book: Sound and Hearing - Stevens, Warshofsky that the higher the intensity of the stimulus the lower the pitch as felt on our mind. So we sing what we think is the correct note but we sing flat. (flat by a few cents which is very annoying). So how does a grea world class singer sings in tune? Who knows? Could it be that they on purpose sing a bit higher and judge correctness in real time not by the pitch itself but by eliminating beats like a proffesional piano tuner? Or do they listen to the backing track at low volume? Or do they have the exact balance of backing track, their voice, by the record producer and recording engineer so that they hear both of them out of tune by the exact same amount? Or are they insensitive pitchwise to higher sound intenity? Anyway i tried to sing and record my voice, see next post, by trying to sign sharper in order to get the end recorded result correct, and it worked. Vicky commented also on real time experiments with my or her voice while playing the piano that when we increased our pitch untill we got it right it did sound very pleasing and bright, happy as sunrise. Trying to repeat the good result while hearing the same piano not or chord, it somehow feels as if there are 2 pitches to choose from and you have to choose the less obvious one. Go figure...Maybe it needs countless hours of training, is this what the greatests singers of all time do?