I think the updated wording for the Noble Brigand is actually less clear than it was before. Previously, when buying, the attack happens but it isn't playing an attack card so it cannot be reacted to by Moat or similar. This is consistent with on-buy "attacks" such as Ill-Gotten Gains.
Now, "do its attack" is ambiguous. "Do" is not a clearly defined word (unless it does clarify in the revised printing). It sort of sounds like you could react with Moat. But I would still be inclined to say you cannot react because it is not playing an attack card.
If the intent was that you can react when it is bought, it would likely say "when you buy this, play it" (I know, that gives you an extra coin, but maybe that would be a benefit to offset the fact that people can now react to it).