Liberals pretend to support black candidates?

Noam Scheiber points to working paper, SOCIAL DESIRABILITY BIAS IN ESTIMATED SUPPORT FOR A BLACK PRESIDENTIAL CANDIDATE, which attempts to figure out the Bradley Effect by guaging avowed vs. implied support. Mark Blumenthal of Myster Pollster has an interview where one of the authors explains the methodology and touches upon some confusing issues....

To a great extent I think this is the sort of thing which should give us caution about overreading from social science; you might not be smoking out the dynamics which you think you are smoking out. I've put the results from the most relevant table below the fold; remember that "True Support" is a calculated projection, and if you are curious about p-values just go to the paper itself.

Group True Support Avowed Support Difference
Total .70 .84 .14
Female .76 .87 .11
Male .64 .81 .17
White .69 .83 .14
Black .79 .94 .15
Other, non-Hispanic .87 .70 .17
Hispanic .55 .86 .31
Less than HS .44 .74 .30
High School .57 .81 .24
Some College .77 .90 .13
College or more .92 .86 -.06
18-29 .98 .87 -.12
30-44 .48 .86 .38
45-59 .83 .82 .-0.003
60+ .54 .81 .27
Urban .71 .85 .14
Non-urban .64 .80 .16
$49,999 .68 .81 .13
$50,000 .71 .89 .09
Voted in 2004 .77 .86 .50
Didn't vote in 2004 .28 .78 -.56
DK/can't remember 1.26 .70 .34
Hardly or never .47 .81 .34
Always or often .80 .85 .05
Liberal .70 .89 .19
Moderate .71 .79 .08
Conservative .73 .85 .12
Democrat .60 .87 .27
Independent .72 .84 .12
Republican .87 .81 -.06
Other party .24 .85 .61
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High SES or Republicans are actual closet supporters with negative difference. Cute!

It's worth pointing out that the results for Dems are altered by a score of .32 among people identifying as "Not very strong Dems", which is highly suspicious (Table 4 - all three other categories have >.75 true support). I smell an artefact.

The list comparison method that they use to determine "true support" is cool, but it may have problems. It is possible that the new, added question will "prompt" the reader to change his attitude towards some of the other questions.

In particular, while they do mention a possible "anti-Obama" effect, they don't discuss a possible "pro-Obama's-money" effect. One of the statements is: "I think Presidential campaigns are too costly." I find it plausible that some Obama supporters would agree with this in general. However, when the new statement is added ("I am willing to support a black Presidential candidate"), they may well spontaneously assimilate the black candidate with Obama, who I understand raised enormous amounts of money for his campaign; this, in turn, may alter their attitude towards "costly Presidential campaigns".

The result would be a relative decrease in the number of "agreed" statements, which under their design would be wrongly interpreted as a lower support for Black candidates.

Or did I miss something?