There is no such requirement - indeed, the only job which is restricted to people who are born in the US is that of President of the US. Any other job is open to anyone who was born anywhere.
Maggie Gee - pilot - was born in 1923.
James Peck - pilot - was born in 1912.
Dennis Mitchell - pilot - was born in 1918.
Rajesh Pilot was born on 1945-02-10.
Jens Müller - pilot - was born in 1917.
Sachin Pilot was born on 1977-09-07.
Louis Pilot was born on 1940-11-11.
Henry Maddocks - pilot - was born in 1898.
William Ash - pilot - was born in 1917.
Glen Edwards - pilot - was born in 1918.
Roger Peterson - pilot - was born in 1937.
Mike Sullivan - pilot - was born in 1970.