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ESRogs comments on Bitcoins are not digital greenbacks - Less Wrong
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Oh, I think I understand part that I didn't before. The reason you put dollars in quotes in the original post is because Alice is essentially creating a new currency with her transaction and calling it "dollars". If Bob uses the same name (and if Alice hasn't cleared out her transaction with an equal and opposite transaction yet), then the proposed system will require him to use the same conversion rate.
Is that right?
Exactly right. I might have done better to create a fictitious name for the currency, but I figured "dollars" would be suitably generic because there are many different countries also using the term. Note that you can have unlimited different currencies each with its own rules and starting point. This could also be used to mimic stock or other intangible assets.