Well if they do operate as a government organization, then they're subject to the same rules. They need to obtain a warrant if they're going to arrest or detain someone. They also need probable cause and that has to be granted by a legal authority. They can't grant it to themselves. That's why there are certain drug cases that get thrown out because without a warrant, it's inadmissible.
And even if Xavier was working with the Avengers, he was not a member of the team. It was never stated outright that he was part of them or that he was granted the same authority. He still mostly coordinated with the X-men and the Jean Grey Institute. A citizen just working with the authorities can't be granted the same privileges as the authorities without some kind of legal standing. The absence of such standing in this case makes your assertion unreasonable and not pertinent to the case at hand.
It actually does matter because this isn't like someone willfully ingesting alcohol. If someone becomes intoxicated unwillingly or by accident, you can't say they're acting with intent. As previously stated, intent really does matter in the course of a crime. That's the difference between Second and First-Degree murder. It's also the difference between Voluntary and Involuntary Manslaughter. Being given money on an error isn't a useful analogy because you're still in a sober state of mind. The Phoenix Force does not put people in a sober state of mind. That is fairly well-documented. There are too many instances of the Phoenix clouding the judgment and perceptions of others to claim that Cyclops was completely coherent. It doesn't matter whether or not he knew the risks. Once the Phoenix was in him, he wasn't in a clear state of mind anymore. Nobody in the Phoenix Five was in a clear state of mind. When you're not coherent, you can't be expected to assess all the risks, especially if it's a result of something you didn't intend.
That's not really relevant to the case in question here, which is the murder of Charles Xavier and Jean Grey's destruction of the D'brai. What Cyclops knew about the Phoenix Force doesn't make him any less vulnerable to becoming intoxicated by it. You also have to account for the stressful situation he was under while acting as a Phoenix host. I think he understood that if kept in the right situation, Hope could manage the Phoenix Force. And when under the right situation, he wasn't inherently violent and neither was the Phoenix Five. They were intoxicated and incoherent, not unlike those under the influence of drugs. But then the situation changed. They were attacked. They were provoked. They didn't throw the first punch. The Avengers did. They helped create the stressful situation that led to Xavier's death. And I think that level of provocation is the key detail in this issue.