More is not always better and I really see no good reasons to split between different kind of information, being them relationships, statistics, or whatever. Just an option for not giving any information that it is not given for the Neutral (null) player (thus comprising not being in the politics panel and in the players tab) should be good enough.
This doesn't even need to be an option, by the way; it may be related to the player having no phases assigned (which would be consistent with the player being, thus, alike to the Neutral one).
Also multiple options, side by side, would give pointless possibilities. For example, I don't think you'd ever want to hide any information about a player while offering it as selectable, do you?
At most, the levels are going to be 3:
1- Players you want to select and have info.
2- Players you don't want to select, but still want to have info.
3- Players you don't want to select nor have info (like the Neutral player in NWO etc.).
I still wonder if number 2 is even much of an item. What's the problem about assigning those players to the AI (maybe even to Nothing) and leaving them selectable, even if you are not supposed to ever select them. Telling a player it is supposed to be not selectable is already done by having it defaulting to an AI, isn't it?
Then, we could add no options at all, but I still believe the "isHidden" option should be renamed into something more consistent and definite.