The Case anecdote doesn't address her desired usage (at least not as presented in the pdf). Maybe she ends up using the service a great deal more at the flat rate, with it's significantly lower marginal price.
It'd be nice if it laid out her perception of what would be fair (we have roughly one data point, that the hourly rate at the time the conversation happened is unfair) and what the economics looked like for AOL (perhaps they could have substantially reduced the hourly price but were good at math and figured that a flat rate was the more profitable path).
The flat rate would have been a guaranteed higher monthly bill that what she was paying at the time, for as you point out potentially higher usage. But if her desired price to pay was $20, and her average monthly bill was n, where n is below $20, why wasn't she already using the service more, at the rate of $20-n?
And, again, the AOL anecdote was an illustration, not evidence. See the truffle study, we know more about this than your response suggests.
So we have an anecdote about marginal pricing going from $1 or $2 (or more) to $0 being used as an illustration that people don't like metering.
If AOL had costs of $0.20 an hour, her perception that their pricing was a ripoff probably wasn't ridiculous.
(I'm not trying to refute you, I was making the perhaps not very useful argument that the anecdote was not a good illustration, because it left too many loose ends. It's compelling because AOL is famous and her behavior is easy to cast as ridiculous, but it wouldn't be real surprising if it was told in a way that was useful to AOL.)
It'd be nice if it laid out her perception of what would be fair (we have roughly one data point, that the hourly rate at the time the conversation happened is unfair) and what the economics looked like for AOL (perhaps they could have substantially reduced the hourly price but were good at math and figured that a flat rate was the more profitable path).