I can't link my own screenshots showing my old 965 right now, but you're pretty much correct. Phenom II doesn't have enough power for H264 4K video.
Once I get home, I'll link you some. I managed to play 4K content using LAV+CUDA and a GTX670 (experimenting of course). That's as close as you'll get to 4K using a Phenom II.
Cheers!