Read my earlier post more carefully.
You jumped the gun and assumed something I did not say.
Of course a clock runs faster in a plane at higher altitude than lower altitude.
I was talking about when the observer 'observes' the other persons clock.
OK think about it like this.
As you fall through the event horizon you can only observe events in which the light can get to you.
i.e. only light rays that end up on your PAST light cone can you observe.
Distant future events cannot get in your past light cone THUS you do not see the universe live and die in your eyes as you fall through.
Sorry if I wasn't clearer. This is hard to explain without drawing light cones and embedding diagrams.
See Wald's book.