Charisma or other stats have very little influence on dice rolls, if any at all. Maybe it's just bugged, and the logs doesn't show anything about these rolls (just fight related), so remains a mystery.
It's all about just a nice random dice roll and then good luck the next playthrough, if you intend to replay it ever, otherwise you either reload or have to enjoy the failure. No other way for now.
For any skill related to Charisma (Persuasion, Intimidation, Deception) it certainly does. It lowers the target (DC) so it's not as obvious, but if you try the same thing with 2 different characters you can see the target change. I had to use Wyll a lot for starting conversations to take advantage of his high Cha. That being said, there certainly are bugs (maybe just visually) - I've seen succeeds where I rolled below the target and failures where I rolled above. I think I read that things like Bless or Guidance don't show up correctly but work under the surface.
