Why HD broadcast camcorder still pictures quality (still frame from video) beat out DSLR?
My guess, what you are seeing is most likely the result of the better color detection and processing with the sensor and image data and the better depth of field provided by a high quality professional lens.

There is far, FAR more to image quality than simple resolution.  The color accuracy of the sensor, the dynamic range, shadow detail, vibrancy and contrast of the processed image, the reduced amount of aberrations as a result of better optics, the better quality of out of focus parts of the image due to better aperture designs, the extra background blur as a result of wider open apertures, etc, etc, all impact the image quality substantially, especially for viewing on a screen.

Unless you are printing the image or zooming in on it, a 1080p HD camera has the same resolution as a DSLR when you are displaying it on a computer screen (since the computer screen itself likely doesn't display much more than 1080p, possibly even less).  So for looking on a screen, the other factors are the only thing that matter and any professional camera will far outweigh it.

Also note that a good DSLR will beat the pants off even a high end video camera in terms of image quality for still images, but you need to have a good quality DSLR and a good quality lens to beat a professional quality video camera (at the 1080p kind of resolution).  

You shouldn't expect the image quality to be better on a camera which costs, in total, less than some of the batteries for the massively more expensive video camera, but I'd put the still image quality of my 5D Mark iii and 24-70 f/2.8 II optics ($6,000 total) up against any $100,000 camcorder you want to bring out.  Even for video, Arri cams will beat it, but shooting RAW footage, it's only a slightly noticeable difference to a professional eye between the RAW video that the 5D Mark iii ($3,500) can shoot versus footage from the $50,000 ARRI camera.