Quite a good solution for the logout problem:

Just tell browser that it is successfully logged in!
This works as follows:
1. User clicks logout button
2. Script sends 401 Header
3. User does NOT enter a password
4. If no password is entered, script sends 200 Header

So the browser remembers no password as a valid password.

Example:

<?php
if (
       (!isset($_SERVER['PHP_AUTH_USER']))
    ||(
           ($_GET["login"]=="login") 
    && !(
             ($_SERVER['PHP_AUTH_USER']=="validuser") 
             && ($_SERVER['PHP_AUTH_PW']=="validpass")
           )
        )
    ||(
           ($_GET["logout"]=="logout") 
     && !($_SERVER['PHP_AUTH_PW']=="")
        )
     ) {
Header("WWW-Authenticate: Basic realm=\"Realm\"");
Header("HTTP/1.0 401 Unauthorized");
echo "Not logged out...<br>\n";
echo "<a href=\"index.php?login=login\">Login</a>";
exit;
} else if ($_SERVER['PHP_AUTH_PW']=="") {
echo "Logged out...<br>\n";
echo "<a href=\"index.php?login=login\">Login</a>";
exit;
}
?>