I don't think you should read too much into our choices. The main objective was to have an application that was reasonably realistic while being relatively straightforward to set up and describe in the "getting started guide".
We chose EclipseLink JPA instead of Hibernate because it is the RI for JPA 2. We chose H2 over MySQL simply because it is is easier to embed in a simple application.
Of course, you are the ultimate judge of the suitability of particular technologies to your projects, but we would say that H2 is most useful for testing and nowhere near the maturity of MySQL. However, EclipseLink JPA should be a good base for a real application.