The colormatrix is correct, that's a range issue.
Your footage is TV levels, but is being decoded as PC levels, that's my closest guess as to why it gets that look.
I'd first make sure you have a proper playback setup: uninstall all your players and then install CCCP (
http://cccp-project.net/ ).
If after rebooting and repairing CCCP in the CCCP Settings you still get the wrong range in Media Player Classic Home Cinema, come back here.
PS: The colormatrix is set on auto by default. That means it's autoguessed based on the resolution. A 960x720 gets autoguessed to bt709, as per ffmpeg standard, anything that is larger than 1024 and/or taller than 600 is considered HD.