Hoogo, thanks for the Dalai Lama pix... a neat test of cleverly designed "trick" images, but not exactly what I am getting at here.
I tried this:
Tool->Color->Convert With Color Profile, Dest. Profile = ProPhoto RGB
This leaves the appearance of the image unchanged, but changes the numerical values of the pixels:
(255,0,0) -> (179,70,26)
(0,255,0) -> (138,237,77)
(0,0,255) -> (85,34,236)
Then I try the Gaussian Blur as before, and get this:
Visually, the image looks
much better, but now the pixel values are all messed up. My understanding is limited, but I'm guessing the "color profile" is somehow embedded in the picture, and the web browser reads this and uses this to "reverse engineer" it for proper display. If I take a screen cap of the above image, I get this image, which seems to have no color profile:
You can see that the pixel values are closer but not quite what they started as.
I'm pretty confused at this point, but I'm have doubts that the default behavior is correct.