Using Rawker to process the raw files and comparing the resulting jpgs with the camera created jpgs gave some interesting results and shows some of the things that are going on.
In this first comparison the Rawker file is slightly bigger, and reveals more. It has slight vignetting. The colours are very similar and both files exhibit burnt out highlights in the white cloud. Overall colour is pretty similar.
The second comparison shows that at default sharpening settings, both are pretty similar. On the originals the Rawker conversion is very slightly sharper though not by much.
I put this comparison together to check out the CA and fringing. But as you can see something else has happened. The two areas aren't the same size though they contain the same information. There is some warping or perspective correction that has been applied to the in camera jpg. In terms of CA and fringing the camera jpg is slightly better, but both are pretty bad.
Intrigued by the previous result I overlapped the two images, "locking" them on the bench - i.e. the area within the red rectangle. As you can see, quite a lot of correction has gone on.
So this gives some idea as to what Panasonic are doing in-camera to "correct" what the lens is recording. It really isn't a huge amount and the Rawker processed file is perfectly fine. There's nothing there that I couldn't do myself in Photoshop. Its also a no worse result than I've obtained from many lenses. I've had £1000 Canon lenses that were worse than this.
The idea that Panasonic are making massive software corrections to compensate for a not very good lens, isn't really apparent here. Its interesting to see what goes on though. In terms of this particular lens, I generally use Photoshop Camera Raw, and that seems to produce the best result. The main problem I see with the 7-14 is the fringing, which although not unusual in very wide angle lenses is nonetheless something I could really do without.