I agree with all of that.
You bring up an interesting point, that is, what to do with facts that counter one's point of view. In a discussion, things that counter your point of view are just as important as the things that support it. When it comes to debates, things become trickier. In an honest debate, I think it best to acknowledge the counter evidence and then discuss why your point of view is still relevant and should prevail (similar to the process that should go on inside of one's mind when formulating their viewpoint to begin with). All points and counterpoints are acknowledged, weighed against one another and the debate goes from there. This has the advantage of maximizing the chances of arriving at "the truth". The ideas that result from such a process are well informed and grounded. This is my preferred method.
In a win at all cost debate (such as politicians vying to be elected), often the opposite is true. Admitting or acknowledging counter facts is risky because it can "lose" you the debate. Someone who presents themselves and their side as strong and infallible is often conflated with someone who is right. Important factors to consider are the format of the debate (how long you have to speak, how deeply topics are discussed, etc.), the goal of the debate, the audience and so on. Acknowledging and thoughtfully considering counter facts can be seen as a weakness by a general audience, especially if not everyone debating is willing to do so. The advantage of this method is that by not allowing counter facts to take a foot hold, your stance appears stronger to the audience and you are more likely to walk away with the victory (such as getting the vote and being elected). The weakness of course is that the we do not move towards the "truth" and in many cases can actually regress. Absolute truth is pushed aside in exchange for garnering support to your side.
In truth, we usually have a combination of the above and the thing that differs is to degree to which each school of thought sways the exchange.
