I ran into the same problem with a similar thematic icon consisting of a small symbol on a solid background. The solution is to select an unused color and use it for the lower left corner of the image, which the ClickOnce installer will use for transparency. In this case, and in the case of my image, the color that he collected was for the most part the image, so the result was shown above.

I found that I need to change the color of the lower left pixel in our icon so that it is a different color than the rest of the background so that the ClickOnce setup dialog box displays the image correctly. 
The result is what we see below, it treats the black pixel as the color used for transparency.

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