As far as needing a stronger bit for riding on loose rein, that’s not true. What is true is that signals in a curb bit can be given by just starting to let the shanks swing, with the rein still loose. On the other hand you could ride a really well trained Western horse in just a rope halter if he really knew neck rein and seat aids.
It is true however that if you want to ride on clear contact English style it’d better to have a mild snaffle.