Consider the question Is there any point in time at which someone can not identify which cards they own? The problem with words is that they need definitions. So let us be very clear about two different definitions of the same word that are tricking us up.
- Time: the indefinite continued progress of existence and events in the past, present, and future regarded as a whole. Typically measured in seconds, minutes, or hours.
Clearly, a "point in time" is therefore defined as the instant in time corresponding to some measurement. For example, January 25, 2015 AD 10:45:12.134 AM or something like that. But I would like to propose an alternative definition of time: instead of measuring it in minutes, we measure it in terms of the game state.
It takes seconds or minutes to shuffle a deck, but in terms of the game state it is an instantaneous action. So if players did not use sleeves, or used the same sleeves, there may indeed be few seconds where it was unknown which card a player owned. I suppose you could Act of Treason another Jeskai Infiltrator, and you both use the same sleeves, and they're both in mint condition. But realistically, a simple inspection of the cards will quickly reveal ownership regardless of what sleeves there are.
Because it is an instantaneous game action, there is no point in the game where a player cannot readily identify what cards are owned by what players.
So let us focus on the questions being asked:
Can Anthony desleeve both manifested cards, or otherwise manipulate them so that they cannot be differentiated?
Answer: cards may be desleeved with the owner's permission, but they must be able to be identified by all players who the owner is. So if you want to desleeve for purposes of obfuscating the owner, that would not be okay. If you desleeve for some other reason (I don't know what) I suppose it's no different than any other time. (Maybe you're alergic to Ultra Pro sleeves or something?) But if you remove that differentiating factor, you must provide some other differentiating factor.
Assume the cards are not sleeved to begin with, or Nathan is colorblind, so that Nathan is unable to differentiate between the two face down cards. Is Anthony obligated to tell Nathan which card is the card that he owns?
This is appears to be up in the air, but I assure you it is not. The tournament rules specifically state:
If a player is ever unable or unwilling to provide free information to an opponent that has requested it, he or she should call a judge and explain the situation.
While ownership of the card is not explicitly listed as free information, the definition of free information is
information to which all players are entitled access without contamination or omissions made by their opponents.
Now, I believe it is clear that "public" information means "free" information. I cannot imagine any definition otherwise. And as we know, ownership of a card is "public" information. The only logical conclusion is that it is a form of "free" information that the guide simply has not provided.
Specifically, we know it cannot be private information, because that public is the opposite of private and that would just be absolutely silly, and that would make the only other alternative derived information. This is defined as
Information to which all players are entitled access, but opponents are not obliged to assist in determining and may require some skill or calculation to determine.
Because the shuffling should have randomized the cards, you have no actual way of knowing by simply calculating and inspecting the visible game state which card is yours. (Especially if you do the unsleeving, or you don't play with sleeves, or you play with identical sleeves.) Derived information, by definition, can be calculated without the assistance of your opponent and merely by inspection of the game state. So this information (ownership) does not meet the qualifications of derived information. If it is not derived or private, it must be free. It's the only type of information that meets all the criteria, and is in line with the Fate Reforged FAQ.
Further evidence, which has that "Because Tabak said so", is taken from this question:
Jeskai Infiltrator's release notes state "A card's owner is public information at all times." Is public information in this context the same as "Free Information" as described in MTG-TR 4.1 Player Communication?
With the ever snarky answer:
Sure, why not? If, for some reason, you’re trying to split hairs here, stop. :)
So while we're not trying to split hairs (but rather, trying to make sure that other's don't try to split hairs) it's pretty clear that he means to include card ownership in Free Information and just apparently never bothered to update the TR.
Answer: if you are unwilling to give your opponent the ownership information of the cards exiled by Jeskai Infiltrator, you should immediately call a judge and explain the situation.