In particular, singers who come in state specifically that their vocal recordings sounds slightly flat when they thought they were singing in perfect pitch.
So why does this happen? Unfortunately, it is physics and fundamentally integrated to how the ear, skull, and sound transmission work. In other words, it can't be "treated" with surgery or medications.
What other people hear when you sing or talk is air conducted sound that gets transmitted through the ear canal, eardrum, middle ear bones, and ultimately to the cochlea hearing organ (pathway A). Image modified from Wikipedia.
Therefore, when a talker/singer listens to a recording of their voice speaking/singing, the bone-conducted pathway that they consider part of their “normal” voice is eliminated, and they hear only the air-conducted component in unfamiliar isolation (what everybody else actually hears).
SO... what is a singer/talker to do if they are disturbed by the way they sound to others? Particularly, what is a singer to do when they always sing a little flat when they truly think they are singing in pitch?
speech/voice therapy. OR... accept that their voice IS different.
For singers, I highly recommend using HearFones Headsetwhich is a funny looking head device that allows an individual singer to hear what they really sound like and more importantly what the audience would hear! In addition, while using HearFones, the singer would be able to hear himself more predominantly over the rest of the ensemble thus helping him to improve the quality of his/her individual vocal quality output.
Over time, singers will be able to automatically adjust their singing such that they no longer will need such a device to sing in tune with others when in familiar surroundings. BUT... in new environments (new concert hall, outdoor arena, etc), it is not unusual that their singing may become off again...
This is why professional singers often wear earpieces that convey sounds recorded by microphones placed in the audience... and also why they sometimes sound flat and out-of-tune when they don't!
It's also why it is VERY important to rehearse in a new place before a concert.
Of note Dr. Chang was mentioned on NBC news regarding this question in this story.