Which two event are you talking about being simultaneous? The Sun going out and Earthers observing it? Those things will not be simultaneous in any reference frame, because they are "light-like" separated. (ie they lie on a 45 degree line in a Minkowski plot.)
I think what he means is when the light from the sun disappearing arrives at earth, that’s effectively when the event of the sun disappearing happened from the earth’s perspective.