The research on that is pretty clear that it does alleviate congestion, the question is for how long. It can definitely take a while before that extra capacity is used up.
It's certainly not a rule that "adding lanes never helps traffic", that's insane.
Now it would be much better if your city built great transit so people didn't have to drive their car.
What I said was that it will temporarily decrease congestion, but that the effect will disappear over time.
Adding lanes to random places where cars stop due to congestion achieves nothing, and adding lanes to non-congested places that feed the bottlenecks increases congestion.
You can find real examples of those tree kinds.