You're really looking at this from the wrong direction. Your competitor doesn't need to fail in order for your own business to succeed. It isn't a zero-sum game.

It wouldn't surprise me if Netflix had that meeting at some point. What would it cost them to run their own infrastructure? Would that be less than the cost of staying with AWS? Is Amazon exploiting their position as Netflix's hosting provider to unfairly compete with them? Do they fear that they might in the future?

At the end of the day, the answer was very likely a solid "no". Many industries are full of examples of competitors working together to the benefit of both companies. Just look at the aerospace industry.