I'd like to notice that if somebody wants to exclude ability to moderate the comments, it, probably will not work.
In such way there are two ways to do that:
1. Add the new capability "Edit Comment". For administrator it will automatically be checked.
2. If this solution will not work, just comment the line 67 in file wp-content/plugins/advanced-access-manager/mvb_wp_access.php. The line looks like:
add_filter('map_meta_cap', array($this, 'map_meta_cap'), 10, 4);
Sorry for this inconvenience. I'll try to fix this issue for 1.0 version