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Which is, I think, what is interesting about this: All-heads is no more improbable than any other random sequence, but in the case of an all-heads sequence, suddenly we start looking for laughing gods, hallucinations, or dreams as an explanation.
Which is to say, the interesting thing here is that we'd start looking for explanations of an all-heads sequence, even though it's no more improbable than any other sequence.
It is not true that overall all sequences are equally likely. The probability of a certain sequence is the probability that it would happen by chance added to the probability that it would happen by not-chance. As gjm said in his comment, the chance part is equal, but the non-chance part is not. So there is no reason why the total probability of all sequences would be equal. The total probability of a sequence of 100 heads is higher than most other sequences. For example, there is the non-chance method of just talking about a sequence without actually getting it. We're doing that now, and note that we're talking about the sequence of all heads. That was far more likely given this method of choosing a sequence, then an individual random looking sequence.
(But you are right that it is no more improbable than other sequences. It is less improbable overall, and that is precisely why we start looking for another explanation.)
No, that's a very good reason to start looking for another explanation, but somebody with no understanding of Bayes' Rule at all would do exactly the same thing. If somebody else would engage in exactly the same behavior with a radically different explanation for that behavior, given a particular stimulus - consider the possibility that your explanation for your behavior is not the real reason for your behavior.