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The statement, "You should expect that, on average, a test will leave your beliefs unchanged," means that you cannot expect an unbiased test to change you beliefs in a particular direction, as is clear from the original post.
Of course you expect to hold different beliefs after the test. If you didn't, the test would not be worth doing. But you are not more likely to end up at (100% heads, 0% tails) than (0% heads, 100% tails).
On the other hand, if you think it is more likely that you will end up at, say, (0% heads, 100% tails), then you cannot rightly claim that you currently believe the coin to be fair (your 50%, 50% estimate does not reflect your true expectations).
Actually you can:
Shake a box with a coin you know to be biased. Before you look into the box, your belief for heads is, say, 80%. You expect that is more likely that, when you open the box, your belief will change to 100% heads rather than 0%.
I don't think there is an useful way to patch the statement without making explicit reference to the technical definition of Bayesian belief.