I *strongly* recommend you get a good book on EJB (for example the Bill Burke / RMH book from O'Reilly).
The definition of "stateless" in the EJB spec is a limitation upon *you*. The container can do anything it likes! What the spec says is that *you* are not allowed to keep any state *relating to the client* in the bean.
It absolutely was my fault. Even 3.2.1. section of the book says it to me:
"They may be used as JSF action listeners, but cannot provide properties to JSF components for display."