IMHO, the fallacy in the claim of unbreakable one-time pad encryption is the reliance that all computed plain-texts for the key space are equally possible to be the correct plain-text for the cipher text.
Imagine you are being that exists beyond time and space and can experience all possibilities at the same time. I would think that all possible computed plain-texts would mostly look a huge pile of crap, but an exceedingly few amount are going to look like something you recognize, and then one of them will look like an Apple.
Once again, that does not mean one-time pads are not very secure. They are very secure, just not truly unbreakable.
No, a one time pad with a true random key is truly unbreakable.
What you've overlooked is that when your hypothetical Godlike being sees all possible computed plain texts, that consists of every possible message of the length of the cipher text.
Note that what the Godlike being sees when he tries all possible decryptions does not depend on what the message is (other than the length). Thus, he gets absolutely no information from the cipher text (other than the length).
Try thinking about it with a small example and that should help you see it. For instance, do a 3 bit message. We've got 8 possible messages: 000, 001, 010, 011, 100, 101, 110, and 111. Let's say you know that only 001, 010, and 100 make any sense. Alice sends to Bob the encrypted message 110.
When your Godlike being considers all possible decryptions, he gets 000, 001, 010, 011, 100, 101, 110, and 111, depending on whether the key was 110, 111, 100, 101, 010, 011, 000, or 001.
So he looks at these, and picks out 001, 010, and 100 as the only meaningful messages. Now what? He has no idea which is the right message.
Now perhaps he knows that some of the meaningful messages are more likely than others. Maybe he knows that 99% of the time, Alice sends 010. So he will probably be right if he guesses that this message was 010.
However, he'd have had exactly the same chance of being right if he had guessed 010 without even looking at Alice's message!
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