I'm glad you brought this up HCF. I'm getting the same shakey camera problem with outside images on an overcast day here in BC Canada (lots of rain at the moment). I'm using an A75 set to auto and on a stable surface with the lens at it's widest. Like you as soon as I turn the flash to auto the "shakey camera" icon goes away but the images look worse color wise when the flash goes off. If the flash happens not to go off the image looks ok.
Funny thing is that I never noticed the icon with my other A75 (developed a nasty lens noise and was exchanged) under similar shooting conditions. I must have left the flash on auto and the day was just bright enough so the camera wouldn't need it.