Did Romney Promise ENDA Support for Log Cabin Endorsement?

Today's endorsement of Mitt Romney by the Log Cabin Republicans included these two sentences:

If LGBT issues are a voter’s highest or only priority, then Governor Romney may not be that voter’s choice….With regard to the LGBT issue most likely to reach the president’s desk and most vital to many in our community today—workplace nondiscrimination—we are persuaded that we can work with a Romney administration to achieve a desirable outcome.

The language struck The Nation's Ben Adler as "nonsensical," he writes:

While it is legitimate for LCR to say that they care more about tax cuts than LGBT issues, how can they only acknowledge that Romney “may not” be the candidate for a voter whose only priority is gay rights? Shouldn’t that phrase be “would not”? And why is LCR persuaded they can work with Romney to pass a workplace nondiscrimination law?

Adler called LCR's R. Clarke Cooper to find out, and after some questioning about Romney's positions on anti-discrimination legislation, gets to what he theorizes hooked LCR's 'qualified' endorsement:

As I continued to press this point, Cooper blurted out, “Have you met with Romney’s domestic policy team?” And therein lies the answer to how Romney secured LCR’s endorsement. His advisers have privately assured LCR that Romney supports ENDA, even though he so fears the wrath of the religious right that he will not adopt this position in public. (Although ENDA polls very well, major social conservative groups, such as the American Family Association, continue to oppose it and demand that Romney do the same.)

Given that Romney is a reflexive liar, the question then becomes why LCR chooses to believe Romney. For that, I have no answer other than wishful thinking on their part.