They are not competitors. I don't know what Bezos said about it, but Elon Musk said:

"Every time I see Jeff, I ask him why he's not doing more in space."

"Our [SpaceX] competitors are not Paul Allen and Richard Branson, but Boeing, Lockheed, and the big aerospace companies. I'm really glad to see all the activity in entrepreneurial space and hopefully this heralds a new era of space exploration with price and quality improvements similar to other technology arenas."