There are rumors around that it is impossible to use the JIRA API anonymously, even with an instance set up for public read access.
This is not true. I wrote a tiny example tiny project to demonstrate it by retrieving info from a public JIRA instance (the one for Hibernate).
The main source of this confusion: neither the official JIRA API Java client, nor the third-party (and easy to work with) rcarz client ships with anonymous access classes or examples.
Get the bits on Github.