The article doesn't tell the complete story of Cook's position.

I would instead summarize by saying that Tim is not afraid to call out the government on their lack of communication skills, and he admits his discomfort of the position he is in.

Here are some relevant excerpts from the interview [1]

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15:12

David Muir: You have talked to the President before on these issues [yes] of privacy and security. Are you disappointed there wasn't more of a dialog with the administration before this swift action from the justice department?

Tim Cook: Yes.

David Muir: You wish there was more done?

Tim Cook: Yes. And I think there should've been... We found out about the filing from the press. And, I don't think that's the way it should be run. And I don't think that something so important to this country should be handled in this way.

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26:00

David Muir: I'm curious Tim. Did you ever think that you would find yourself at the center of such a crucial national debate?

Tim Cook: No. This is not a position that we would like to be in. It is a very uncomfortable position. To oppose your government on something doesn't feel good. And to oppose it on something where we are advocating for civil liberties which they are supposed to protect, it is incredibly ironic. But this is where we find ourselves. So for all of those people who want to have a voice, but they're afraid, we are standing up. And we are standing up for our customers because protecting them, we view, is our job. And I hope, and I think, I'm very optimistic, I think we will come together. I don't know what will happen. But I think we will come together and there will be one path forward. The US always comes out of these things well. I feel very good that the debate is going on. Even when people disagree with us, it is good that the debate is happening. That's what makes this country so special.

David Muir: And for you, personally, has this been the biggest challenge in being CEO of Apple that you've faced?

Tim Cook: I've faced a lot of challenges. But I've never felt, sort of the government apparatus. And so yes I would say this is right up there. But it's not my sole focus by any means. We're focused on making great products.

David Muir: ... Are you prepared to take this all the way to the supreme court?

Tim Cook: We would be prepared to take this issue all the way, yes. Because I think it's that important for America. This should not be decided court by court by court. If you decide that it's okay to force a company to do something that they think is bad for hundreds of millions of people. Then, think about this for a minute. This case is an awful case. There is no worse case than this case. But there may be a judge in a different district that feels that this case should apply to a divorce case. There may be one in the next state over that thinks it should apply to tax case. Another state over it might apply to a robbery. And so you begin to say, wait a minute, this isn't how this should happen. If there is going to be a law, then it should be done out in the open for people so their voices are heard through their representatives in congress.

David Weir: And if congress decided that there's this small category, this was a terrorist's iPhone. If congress decided that, if the American people signed off on that, you'd entertain it.

Tim Cook: Now let me be clear. At the end of the day, we have to follow the law. Just like everybody else, we have to follow the law. What is going on right now is we're having our voices be heard. And I would encourage everyone who wants to have a voice and wants to have an opinion to make sure that their voice is heard.

[1] http://abcnews.go.com/WNT/video/exclusive-apple-ceo-tim-cook...