That's totally true, but the thing is David is supposed to be a rather jealous guy. As players, we can encourage him to trust Anna more, but the jealousy previously got to the point that Anna started feeling the need to keep things from him just to avoid fights (for instance, she doesn't tell him about Hank grabbing her or Chris continually flirting with her). David's normally a nice guy, but I don't think of him as passive or oblivious. I'm amazed he was even able to contain his anger when Chris made a pass at his wife right in front of him. Granted, it's been well-established that David does have blinders on when it comes to Chris, and he could try to excuse Chris because he had been drinking or brush it off as a joke as Anna tells him to...but that seems more like the kind of self-delusion a passive or oblivious person would engage in. At some point, I expect to see the beast emerge if David's truly the jealous type.
Incidentally, I don't see David ending his friendship with Chris as necessarily stopping Anna and Chris from getting together. If David had exploded or gotten violent, I bet Anna would have been upset with him for acting like a jealous schoolboy. She'd surely have responded to Chris if he texted her some sad message about David refusing to talk to him. If he invited Anna for a coffee so they could talk about whether his friendship with David was salvageable, I could totally see her accepting that offer. Of course, since it's Chris we're talking about he'd probably invite her to the bar for a beer and then try to get her drunk enough to fuck him, but you get my point. Chris already seems to talk to Anna more than David so the "friendship" between the two guys is on thin ice already and fraying more by the day.