Having gone to a minor (read: high school) seminary, I can say this tradition generally applies to any priest, though it has since (thankfully, and before I got there) died out.

Any priest is required to be free of physical defect, and in good health. The current Archbishop of Chicago was refused admission into the diocesan seminary because he suffered from ill health; asthma and polio, if I am not mistaken. Part of the physical examination is to make sure the prospective seminarian has got a pair, and that both have, *ahem*, descended.