One theory as to the verdict being different than the original verdict of "guilty" was that the State did not seek the death penalty. As such, the jury on the re-trial could have been far less conservative since the "no death penalty" advocates would not be disqualified (since the issue was irrelevant).

But the newspaper accounts say this: "Prosecutors could not seek the death penalty because the first trial's jurors sentenced her to life in prison and authorities had found no new evidence."

I suddenly feel dumb. Is that statement correct?

I don't think "new evidence" has any significance. The first jury answered the FD special issue "no." Yates v. State, 171 S.W.3d 215, 216 (Tex.App.-Houston [1st Dist.] 2005).

A second shot at the DP is barred, by Double Jeopardy, if the first jury found the State didn't establish that the DP was called for. Bullington v. Missouri, 451 U.S. 430, 101 S.Ct. 1852, 68 L.Ed.2d 270 (1981).