Oh man, that diver is full of it. I went swimming in a mountain lake last summer and my brain just shut off for a second from the cold. It's a real, physical thing, not just in your head.
That diver must have never dealt with the real physical shock your body goes through. I grew up in a lake town and we had a rule - no one dives in until the water hits at least 60 degrees because anything colder can literally stop your breathing. Your heart rate spikes, your muscles lock up, it's not just a mental thing. People have drowned from cold water shock because their body just gives out before they can even try to swim. It's like saying a broken leg is just a state of mind, doesn't work that way.