I removed JDK 1.7 from the system, but that didn't help. I then removed the jbpm-install from my system and re-installed it. I didn't notice before, but, like you said, the first time you run "ant start.demo", the script compiles from Java files and use them on subsequent runs. So, on my system, it had compiled the sources with 1.7, but afterwards it wouldn't run them on JDK 1.6. Removing and reinstalling jbpm-install and re-running with just JDK 1.6 fixed the problem.
Thanks for all the help.