I checked file permissions. This was a Tomcat secrurity policy, designed to protect the JVM from idiot (or malicious) code. The (basically sound) idea is to prohibit all filesystem access, and open it up on a per-file, per-servlet basis. For this devel box, I'm just going to open it to all servlets, because mine will be the only ones on it.
As Ben mentioned above (below?) keeping each JVM isolated in a hosting situation is not feasible. Makes me question how useful the Java security model really is.