Twitter should look into what happened in this specific case, and somehow (if the posting is right) return the username to its original owner.

But there does seem to be something terribly broken here if it's possible for someone to get another person's Twitter account, and for it to take a full investigation to get it back to the original owner. And for not having better procedures in place, I think that an apology wouldn't be unreasonable.

In general, it seems to me that demonstrating empathy for your customers is a pretty reasonable strategy. Even if they didn't do anything wrong, and before they have finished this investigation, they can show that they care about the people using their system.

I don't think that Twitter could go wrong by saying, "We now see that we need to make it harder for scammers to switch the ownership of a Twitter account, and are looking into how to do so without hurting our legitimate users."