True.  With more active gaits, I think you're supposed to crouch in the stirrups and use the saddle for balance.  I don't know if I'd call riding on a lazy walk "improper" - the gait is just as proper as any other.  I guess I shouldn't assume what they're doing in the class without knowing more... but I know about fatties, and they wouldn't take up something that sounded like much work.