Romney did say (as the Arizona Republic reported, but CNN did not, in the above link) that "Let me assure you that no authorities of my church, or of any other church for that matter, will ever exert influence on presidential decisions. Their authority is theirs, within the province of church affairs, and it ends where the affairs of the nation begin." Conversely, the Republic failed to report Romney's "freedom requires religion" statement.
For Romney, it is clear that he does not agree with Jefferson, Madison, and the Constitutional Convention that the First Amendment protects the nonbeliever as well as the believer (as is clear from their writings, their actions as president, and from earlier drafts of the First Amendment that were rejected). Instead, his version of the Constitution requires everyone to belong to some religion, whether it's a cult founded by a con artist or an ancient world religion. He thinks that freedom and religion always must coexist, despite thousands of years and millions of people worth of evidence to the contrary. (Though perhaps his "requires" is a moral claim, that in order to be worthwhile or good, those things must come together--in which case I'd agree that religion requires freedom, but not that freedom requires religion.)
The Republic also noted another serious defect in Romney's comprehension of the First Amendment:
At the same time, he decried those who would remove from public life “any acknowledgment of God,” and he said that “during the holiday season, nativity scenes and menorahs should be welcome in our public places.”Such scenes are already welcome in public places, so long as those public places are equally open to religious and secular displays by believer and nonbeliever alike. The only thing that is forbidden is exclusively allowing displays by a particular religion, which of course is what many Christians are actually demanding. For such an exclusive right favoring a particular religion or religion over nonreligion, displays must be on private property. It's a simple and fair concept, but the religious right repeatedly misrepresents it and falsely claims to be oppressed because they aren't given special privileges that no one else has, and whines and complains when something happens like a Hindu giving a prayer before Congress. And nobody has tried to prevent Romney, Giuliani, and the rest of the presidential candidates from their repeated references to God, despite the transparent phoniness of most of their claims to faith. It's clear that most of them are simply signalling to the religious right that they will continue to be granted special preferences, rather than truly displaying what they believe--their records of political expedience and lack of integrity speak more loudly than their words.
With people of such opinions in political power, explicitly willing to deny political freedoms to those who are nonbelievers and grant special privileges to anything calling itself a religion, it should not be surprising that some people will, out of pure expedience and self-defense, take steps to convert atheism into a religion. Yet that should be unnecessary under our Constitution, as a Washington Post editorial on Romney's speech agrees.
UPDATE: DI Fellow John Mark Reynolds comments on and posts the entirety of Romney's speech, which is certainly better than the quotes above would suggest--he does criticize the establishment of religion in the Massachusetts colony, for example: "Today’s generations of Americans have always known religious liberty. Perhaps we forget the long and arduous path our nation’s forbearers took to achieve it. They came here from England to seek freedom of religion. But upon finding it for themselves, they at first denied it to others."
UPDATE: P.Z. Myers and Greg Laden each give their take on Romney's speech. And here's Christopher Hitchens' view.