One of the prime functions of the bicep is to twist the hand, wrist and forearm as well as bringing the lower arm in and towards the body (curling towards= rows, up-rows, chins, actual curling, etc). If you punch a heavy bag the correct way or practice martial art fist/palm strikes you will be twisting the arm in it's natural path, which affects the bicep strongly and where you gain the most power. Still rings, high bar, parallel bars, mounting horse and even floor exercises demand much from the biceps in the way of actuall curling (even partial), static holds and negative releases. Most of the muscle fiber (think of them as little cables, the more muscle stress the more cables are called into action) becomes much stronger and larger, due not only to the workload put upon it but the increases circulation (better blood supply) which feeds the muscles with a ready supple of freshed nurishment. So gymnast get super strong while also gaining quality muscle mass. Straight arm work will call upon the bicep/tricep's strongly but not to the extent of being responsible for major bicep muscle growth. I can never say that any one is completely wrong about anythig, so prehaps the coach was misqoited and just has a different view on matters.
I've suggest this before quite a few time; using gymnastic rings or the one's that can turn 360 degrees, are a superior way to build outstanding lats because they follow the natural strength curve of a overhead pulling/chinning motion. Much easier on the wrist, elbow and shoulder joints. Also one of my better result producing workouts in the past was to SS chins with Dips. Covers just about all the major upper body muscle groups. I have always favored weighted dips over flat or incline presses for chest/delt/arm mass, but that's just how my body respones. Everyone has different results from different methods. Good Luck.