I'm not sure if sticking to the rules would make for a better Acquisitions Inc game - considering that the focus is on a comedic and entertaining version of D&D, played by geek celebs with audience participation. I mean, sure, they could be much more accurate to the rules; but would that make it more fun? I can't see how anyone goes into AI and thinks, "Oh, this very accurate and serious depiction of D&D got the rules wrong for sneak attack. I can't see how they got that wrong". Now, something with a completely different focus - say, 'D&D done by people who know how to act' - might want to be more accurate with the rules.
Thanks to this thread, I've got Critical Role saved on my Youtube. I might give it a try. I watch AI while painting Warhammer stuff, mainly, since I like to have funny and interesting stuff (which doesn't require my eyes) for background. For that purpose, I've found AI to be great. The humour is really funny - though a lot of the jokes are so intensely American, I've got no idea what they mean - and while there is essentially no roleplaying going on, it serves as an amusing version of a beloved hobby. I guess that I think of it like a comedy sketch show that happens to be themed around playing D&D. I've got a game on Thursday, when I'm showing D&D to a bunch of fellow PhD students in my department, and I'm half tempted to show them a clip of it just so that they know 'how D&D games should look'. I probably won't though, since launching straight into a description myself of how the game works will be less jarring.