I think you've gotten fear confused with panic. Fear is indeed a learned behavior, panic is not. Panic is beyond rational thinking, it is what gets people who save drowning people dead. Panic is what gets normal humans dead when in bad situations. Panic is not learned, it saves your ass at all costs -- or gets you killed.
They’re just wrong. Neither panic nor fear is learned behaviour. What one panics about or fears is in part learned. But there is still a lot of instinct at play.