From what I've researched on this subject, there was talk of a constitutional amendment banning same sex marriage, which would have been able to pass at the time. If DOMA was rejected, then the amendment would have happened, and would have been considerably more difficult to later repeal. When you look at how things work in politics, DOMA isn't as damning as one would imagine. Something anti-gay was going to happen, and this was the best of the worst. The same email you cite as your source also says that Hillary does not want to double down on this event, and mentions her opposition to the bill once it went to court.

We have to be careful when rationalizing legislation that restricts human rights by saying that another alternative could be worse. An example I will give is another Clinton gem - Don't Ask, Don't Tell.

Bill was able to collect some points, look like he was catering to gay rights, by having something that, on the surface, looked like he was progressing human rights.

But, as somebody who was in the military at the time, it was politics without any substantive change in practice. Upon entering the military, they couldn't ask if a person was a homosexual. Great, you don't have to lie to get in. However, people were still kicked out for being caught with their boyfriend. People who might have confided in a friend that his roommate was actually his lover were gone. If a letter back home was found and read, a man writing his letter to his boyfriend was kicked out. Even a few too many beers at a party could expose secrets that end your time in the military. You no longer had to lie to get in, but it kept firmly in place the more difficult part of living a lie to stay in.

So, with no real change in policy but lots of hoopla over the politics, DADT was kept around far too long. "We quit asking them, what more do they want?" One could argue that the "compromise" caused longer suffering than if the progressives would have just held out for something of substance.

The same goes for DOMA, in my opinion.