Upon attempting to set matrix-based security with Jenkins' own user database, where the two existing user accounts were given permission to do anything, the Authenticated group had overall read and job read, and anonymous users had no permissions, the following error occurred:

hudson.security.AccessDeniedException2: anonymous is missing the Overall/Read permission
at hudson.security.ACL.checkPermission(ACL.java:59)
at hudson.model.Node.checkPermission(Node.java:435)
at jenkins.model.Jenkins.getTarget(Jenkins.java:3824)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:674)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:876)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:649)
at org.kohsuke.stapler.Stapler.service(Stapler.java:238)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:848)
at org.eclipse.jetty.servlet.ServletHolder.handle(ServletHolder.java:686)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1494)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:123)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:114)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:48)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:168)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at org.kohsuke.stapler.compression.CompressionFilter.doFilter(CompressionFilter.java:49)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1482)
at org.kohsuke.stapler.DiagnosticThreadNameFilter.doFilter(DiagnosticThreadNameFilter.java:30)
at org.eclipse.jetty.servlet.ServletHandler$CachedChain.doFilter(ServletHandler.java:1474)
at org.eclipse.jetty.servlet.ServletHandler.doHandle(ServletHandler.java:499)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:137)
at org.eclipse.jetty.security.SecurityHandler.handle(SecurityHandler.java:533)
at org.eclipse.jetty.server.session.SessionHandler.doHandle(SessionHandler.java:231)
at org.eclipse.jetty.server.handler.ContextHandler.doHandle(ContextHandler.java:1086)
at org.eclipse.jetty.servlet.ServletHandler.doScope(ServletHandler.java:428)
at org.eclipse.jetty.server.session.SessionHandler.doScope(SessionHandler.java:193)
at org.eclipse.jetty.server.handler.ContextHandler.doScope(ContextHandler.java:1020)
at org.eclipse.jetty.server.handler.ScopedHandler.handle(ScopedHandler.java:135)
at org.eclipse.jetty.server.handler.HandlerWrapper.handle(HandlerWrapper.java:116)
at org.eclipse.jetty.server.Server.handle(Server.java:370)
at org.eclipse.jetty.server.AbstractHttpConnection.handleRequest(AbstractHttpConnection.java:489)
at org.eclipse.jetty.server.AbstractHttpConnection.headerComplete(AbstractHttpConnection.java:949)
at org.eclipse.jetty.server.AbstractHttpConnection$RequestHandler.headerComplete(AbstractHttpConnection.java:1011)
at org.eclipse.jetty.http.HttpParser.parseNext(HttpParser.java:644)
at org.eclipse.jetty.http.HttpParser.parseAvailable(HttpParser.java:235)
at org.eclipse.jetty.server.AsyncHttpConnection.handle(AsyncHttpConnection.java:82)
at org.eclipse.jetty.io.nio.SelectChannelEndPoint.handle(SelectChannelEndPoint.java:668)
at org.eclipse.jetty.io.nio.SelectChannelEndPoint$1.run(SelectChannelEndPoint.java:52)
at winstone.BoundedExecutorService$1.run(BoundedExecutorService.java:77)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1157)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:627)
at java.lang.Thread.run(Thread.java:863)

This seems to be the same issue as 19010, but the given fix is merely to give anonymous users read access. The fact that anonymous users must have read access seems to be a bug in and of itself.