Pretty much, yes. (Not necessarily exactly equally unlikely -- human cheaters and perfect unbiased uncorrelated coin flippers don't produce the same output. But if you've got some arbitrary 100-long sequence of coin flips, you don't get to say "Alice must have cheated because that sequence is unlikely by chance"; it's unlikely by cheating too for the exact same reason.)
Ok. I think part of the issue [ETA: with our mutual understanding of each other, not with you] is that you're focused on the "You're lying" part of the conversation.
I'm considering it in the context of this: "My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?"
Granted, his observations have N bits of information (at least), the same as the situation with cheating, and it's at least as improbable that he'd observe a given sequence of length N when s...
Alice: "I just flipped a coin [large number] times. Here's the sequence I got:
(Alice presents her sequence.)
Bob: No, you didn't. The probability of having gotten that particular sequence is 1/2^[large number]. Which is basically impossible. I don't believe you.
Alice: But I had to get some sequence or other. You'd make the same claim regardless of what sequence I showed you.
Bob: True. But am I really supposed to believe you that a 1/2^[large number] event happened, just because you tell me it did, or because you showed me a video of it happening, or even if I watched it happen with my own eyes? My observations are always fallible, and if you make an event improbable enough, why shouldn't I be skeptical even if I think I observed it?
Alice: Someone usually wins the lottery. Should the person who finds out that their ticket had the winning numbers believe the opposite, because winning is so improbable?
Bob: What's the difference between finding out you've won the lottery and finding out that your neighbor is a 500 year old vampire, or that your house is haunted by real ghosts? All of these events are extremely improbable given what we know of the world.
Alice: There's improbable, and then there's impossible. 500 year old vampires and ghosts don't exist.
Bob: As far as you know. And I bet more people claim to have seen ghosts than have won more than 100 million dollars in the lottery.
Alice: I still think there's something wrong with your reasoning here.