These were what I was thinking of. I believe they asked liberals to answer a political question about their own beliefs, and then again to answer for a 'stereotypical' liberal and conservative. The liberals were not accurate for anyone. The conservatives were able to better match the 'average' for those groups. In other words, the study claims that this means they are better able to put themselves in the shoes of the 'other' side

> The participants were 2,212 visitors (62% female; median age 28; only U.S. residents or citizens) to ProjectImplicit.org, where they were randomly assigned to this study. All participants in the research pool had previously filled out demographic information, including sex, age, and political identity (7-point scale, strongly liberal to strongly conservative). 1,174 participants self-identified using one of the three liberal options, 538 chose the “moderate” midpoint, and 500 chose one of the three conservative options.

The strong left-leaning bias in the sample makes me suspicious that this sample isn't representative of the wider population. I can't find the raw data, but given the selection method I strongly suspect that the sample is mostly college students.

If so, one hypothesis that might explain the results is that conservatives who go to college of necessity have a stronger understanding of the other side than liberals because they're the minority on campus for many years. If you repeated this study with a more representative sample of conservatives, including conservatives who do not have the opportunity to interact with many liberals, do you get different results?