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Is your TV a Widescreen TV? I'm assuming it isn't.
I have a Sony WEGA 28" Widescreen and this gives me no problems.
However, having also played back The Matrix on my parents 'normal' 4:3 Sony TV, the picture was stretched as you describe. Fortunately, that TV set (which is about 3 years old now) has a 'Widescreen' button, which adjusts the picture to correct the problem.
I *think* I also managed to get rid of the problem using the PS2's settings, but I can't be 100% sure of that.
Oh and by the way if you want to use your PS1 RGB scart cable with your PS2 just pull it out of the back of the PS2 slightly you won't get a green screen anymore but the picture will be composite because of only 15 pins being connected unlike RGB which is 21 pins and gives a superior picture quality. Sony did the green screen to stop piracy.