720p being better for sports isn't a factor in a broadcasters decisions.
Any comments they make claiming such is just PR Spin.
720 is chosen to save money and make more money - it uses a substantially lower bandwidth with the same compression per frame, and that's without taking in to account the 4:3 squeeze that the broadcast signals get - 1920x1080 is transmitted ( radio and cable ) as 1440x1080 with rectangular pixels.
This means they can run an extra side-channel within their allocated broadcast bandwidth, which they charge money to fill with advertorial programming, such as the shopping networks shown here in Australia,
But back to the HDMI,. If the camera is set to output 1080 (i or p) and the Ninja sees that as 720, then either the camera is not sending 1080, or the Ninja is set up wrong for 1080.
If the camera sends 1080, the Ninja should be recording in 1080.
So we're back to, what's the camera set to?
And I did notice the comment about needing to turn off the displays everywhere.
I assume that means in the menus for the histogram and the like, and cycling the info button for the status overlays.
Thank you for that, it reduces my reasons to not buy a K-3 almost in half.