Earlier quoted context omitted.
Yep! That's exactly why. USB-C alternate mode only supports DisplayPort 1.3 and HDMI 1.4b. You'll need an active adapter like you mentioned. Not surprisingly, Apple doesn't sell them, that would be to useful. For future readers, here's one as an example: https://www.amazon.com/dp/B01FIVSC6Y/
Note that one actually says it is not compatible with the new 2016 MacBook Pro.
Odd, works for me. Hmm