Have him quote where it says that anywhere in the rules.
Hint: it only says it when the Shooting Phase starts, therefore you don't count as moving in the movement phase, therefore movement based effects won't work. You're just disallowed most movement in the movement phase, but you don't count as moving until the Shooting phase.
Deep Striking itself does not inherently count as moving and nowhere is that idea supported in the rules.
Also; mod hat
Moving this to Rules Questions - because, y'know, that's what it is.