My interpretation of this advice is that it is creating a necessary loophole for, say, someone's physician to state that a patient should not wear a mask. Maybe it would include people on supplemental oxygen or with respiratory difficulties. Could also include people with injuries on the face.
The point is that it is vague on purpose; it doesn't intend to make any specific claims or allude to a particular condition (if it did, it would state that condition). I would not expect there to be any study of this because the circumstances involved are all going to be "special cases".
An airport isn't qualified to act as everyone's personal physician, and does not feel safe giving medical/public health advice that cannot be overruled, as this could lead to a lawsuit if they were to, say, expel someone from their premises who had a legally protected reason to not wear a mask.
Title III of the Americans with Disabilities Act (ADA) is a relevant law, and includes protections and requires accommodations for those with disabilities.
I did find one public health source (and I'm sure there are others, just using this as a particular example) that has some more specific exemptions which included:
Those who cannot breathe safely;
Those who, due to a behavioral health diagnosis, are unable to do so;
Those communicating with people who rely on lip-reading;
Those who require supplemental oxygen to breathe;
Again, #1 is a broad category allowing for people to get personal opinions from their doctor that their breathing is impaired by a mask, #2 and #3 are likely important from an ADA compliance perspective. You don't really need a scientific study to show that people who communicate with lip-reading can't do so when the people speaking are wearing a mask, or that people with mental health issues with wearing a mask have issues with wearing a mask.