Wives tale? Not quite. Higaonna Sesnei has taught this to adult students. If you train regularly and practice this on a daily basis you can withdraw the testies at will. Once they are within the body no harm can come to them.
Exactly where you get your statistics from is beyond me. "Most attacks happen by surprise and from ambush." Not quite, most are from verbal confrontations which allow you a enough time to withdraw them before physical contact.
I added that section into my initial comment for those that understand the difference between a groin cup that is needed for tuurnment participation.
If you are ever in a physical confrontation on the street and realize that your opponent is wearing a groin cup, they you must also realize that he was out looking for a fight.
Hard case: Get a grip.