Well, technically his argumentation is valid. However, it obviously can't work in real world as such if you're not a sociopath...
The problem is two-fold: First, is logic and the available information enough to make a correct decision in any situation? Second, what should be used as criteria that separates "good" or "correct" decision from "bad" or "incorrect" decisions?
The first issue is the simpler one, and ties to the second one. But starting from the first one, let's take the old example where there's a loose train approaching a group of workers who apparently are not paying attention to their impending death. The train has impact sensors that trigger the auto-brakes when they hit a heavy enough object. You know you aren't heavy enough to trigger the sensors, but there's a hapless big-boned man standing on the platform next to you, and he is heavy enough to make the train brake and save the group of workers ahead.
You can either push the big guy in front of the train, killing him, or you can choose to do nothing and the train will squash the group of workers.
However, logic alone can not dictate the "correct" answer in cases like this, or any other where killing is hypothetically "necessary" for the greater good (personally I fail to see the point in that kind of greater good any way).
The problem with determining your actions with logic alone is that people are not inherently logically accurate beings, and the information we think is accurate may not be so. That means we should be aware that our "logically sound" decisions might not be the "correct" or "best" after events have unfolded, which means we shouldn't blindly do what seems to be logical either, especially in this kind of "the end justifies the means" situations. We can't know if seemingly logical action always leads to the best outcome.
Or rather, it should be taken into consideration when forming the logical response to something. The knowledge of the possible lack of information is information in itself. In the example, it is possible that even if you don't push the big guy under the train, the train will somehow be stopped by remote control or driver getting into controls. Or the group of workers might notice the threat and get away without you killing the big guy.
Or, it might be that the big guy fails to trigger the auto-brakes and the workers are still killed, but now there's an additional victim. Or, the big guy dies but workers would've noticed the threat and saved themselves, but the "logically sound" decision got the big guy killed...
The second issue about what kind of decision is correct is a more complex one.
In my opinion, morals and logic are not enough to go by. Morals are just the code of conduct in a particular community, and logic is not always applicable and with limited judgement capability and information can lead to really bad results. Laws and regulations are not always acceptable either but as long as they are legitimate, I prefer to sticking them but they aren't the highest authority that dictates my decisions.
To make decisions where you can live with the consequences is not possible with just logic and information alone. Or morals alone, or laws or regulations.
What you need in addition to laws, regulations, morals and logic is a set of ethically sound principles. Which is not the same thing as morals. Morality implies the commonly accepted "right" and "correct" behaviour, and can be really misleading - and they can be exploited and misused, even changed, by community authorities like political or religious leaders. Ethic principles, however, need to be thought through by each individual themselves, and are in my opinion the better choice between abiding to morals or ethics. Then you need to apply the ethics to the logic to see what kind of actions are acceptable - not by society, or laws, but by you.*
However, each person really needs to find their own ethical camp, two main ones being utilitarianism and Kantianism. I'm in the latter camp - in my opinion it wouldn't be acceptable to use the Big Guy as means to saving the workers from the impending death by train, even if that action had a chance of affecting positively to the workers' fate. All the unknown factors mentioned earlier would lead to the same conclusion if I were an utilitarian thinker, but that's beside the point. Also, along with information, intuition and instinct are also sometimes needed.
Rationalizing all mistakes and decisions that had negative consequences by saying that they were the logically best option at the time is just bull****, since obviously the logic failed to take into account the fact that information might be flawed or lacking. Not feeling regret or remorse after making a wrong decision is not normal. People make mistakes all the time, and I don't think most people aim to behave illogically. There is some logic (aka motives) behind every decision made, and at the time they obviously seem like correct decisions. So is he saying that no one should feel bad about their mistakes? That makes no sense at all. Feeling bad about a mistake, no matter how correct the decision seemed at time, is how we learn not to repeat the decision in similar conditions. When you make a decision that has negative consequences, it is normal to wish you had chosen differently, or that you could have avoided being forced to make that decision. Especially in situations where the decision affects other people.
*Obviously there are people whose ethics don't work the same as mot people's do, and they need the laws and regulations to prevent them from causing harm to the society...