Image quality of the TS20 is quite poor if you ask me, although video is certainly better than Fuji.
I'm curious what are all the factors you use to evaluate image quality of a camera? Noise? Detail? Dynamic Range? Color Balance? Low-light performance? Seems like you have to take quite a few criteria into account, no?
Based on those criteria, is there a camera in this same class (ultra-zoom compact) that produces significantly better images across most if not all criteria? Or is you comment just IQ in general compared to all cameras. If so, I'd agree, it isn't that great compared to larger sensor cameras or some compacts with much shorter zoom range. If you are saying poor relative to other cameras in the class, do you have some comparison images we can look at? Because if so, I'd like to know what camera it is so I make sure I've tested and compared all the options.
Frankly, I used to be 99% concerned about only evaluating image quality on cameras by pixel peeping over and over. What I found though was that in the field, under a variety of shooting conditions and scenarios, there was a lot more aspects to the camera that were more important than I gave them credit for. I typically read a lot of reviews, forum posts and compare a lot of images. But I've found, there is absolutely no substitute for actually using the camera yourself, especially in your most common shooting situations. I found that in the end, the quality of my photo/video library was maximized by using the camera with the best blend of image quality, video quality, ergonomics/speed, focusing reliability, pocketability, flash performance, settings/features, etc. Start-up speed for example was something that became evident was a lot more important than I thought. Image quality becomes a moot point if you miss the shot in the first place.
The Fuji is a really good camera if you throw out the video issues.
I should note the review referred to by the OP, the video shot demonstrates the issue, but they went really EASY on the camera in my opinion. They panned it very very slowly and when they did zoom in the zoomed in very slow and directly without any side to side movement. If they would have zoomed, then panned, it would really make the camera's video performance look really bad.