A young friend of my parents, now several years into a successful CC career, was rejected as she just failed to meet the minimum height requirement for a UK charter.
Being the determined type, she insisted she was the right height and asked if she got a medical certificate proving she was the right height would the take her. The airline said yes.
So off to the doctors to be measured in her socks, hair down etc.
No problem, just on the minimum height.
Once she got out of the doctors with her certificate she peeled the very thick sanitary towels off the soles of her feet and got in touch with her future bosses.
She has changed jobs more than once and never had a problem since.