While most of the logic here is sound, I really disagree with the wording of the sentence So the author would, presumably, on balance of probability,

While most of the logic here is sound, I really disagree with the wording of the sentence So the author would, presumably, on balance of probability, be convinced that no combination of any 76 coin tosses has ever come up. It does not follow at all. The statement that "Sequence X_i has never been tossed" is independently probable for any long sequence X_i. The author is only making a single statement, and while it's true she has no particular reason to focus on the particular sequence of constant heads her statement is completely logical and very far from being refuted by observing any particular sequence of 76 coin flips unless it just so happens to be 76 heads. The illogical point only arises if we try to take many of these independent statements all at once. If we take some significant chunk of sequences and state they've each all together never been seen before then we eventually must stop feeling that statement is probable. One way to clarify the whole thing is to assign a bet to any given probabilistic statement. The author bets $10k that nobody has ever seen 76 heads. I can bet $10k that nobody has ever seen 76 tails. In each case our expected value on these bets is identical. Someone else could bet 10c on each possible permutation and be guaranteed to win, but obviously forced to distribute his bet. It's not at all illogical for me to feel very confident that your coin flipping sequence wasn't all tails. It's highly illogical for me to believe your coin sequence wasn't in the set "all possible coin flipping sequences of length 76".