This is happening right now with 'Blacklist: Redemption' S1 Episode 6 on NBC on demand in Tucson. 'Veep' (HBO) and 'Shades of Blue' (NBC) last night. We have a contour box as well. not sure of the episode numbers of those.
I have reviewed episodes of Great News and Blacklist: Redemption' S1 Episode 6 and I wasn't able to duplicate the audio video sync you've shared. Is this still happening, if so, please include the series and episode number(s), so we can continue to investigate this.