As you explained in your comment on MDL-10127, the interaction of this capability with the Site Policy 'Full Name Format' works properly in 1.8.1. I tried it, and it does. Thanks!
Getting back to Visitor, it seems that viewfullnames is not applicable. If we are going to allow Visitors into our courses, we will need a way of preventing them from seeing any part of the real names, while at the same time allowing others (teachers and students) to see whatever their capabilities (and the site policy) allow. The forcefirstname/forcelastname hack in config.php doesn't seem to be a solution either, since it affects users who can normally see names.
MDL-8148 asked for a solution to the "anonymization" problem" back in 1.6, and it got wide support. Petr Skoda commented that roles would be the solution. In a later comment (after 1.7 was released) he commented again
there is no capability yet, that would do exactly this yet 