This is the updated working code in stats-profile.php which together with code above in bp-custom.php (buddypress functions.php) gives me the title(s) of displayed user for multiple custom post types.
<?php
if ( is_user_logged_in() ):
query_posts(array(
'post_type' => array(
'post',
'portfolio',
'applicant',
'agency',
'employer'
),
'author' => bp_displayed_user_id(),
'showposts' => 3
) );
?>
<?php while (have_posts()) : the_post(); ?>
<h3><a href="https://wordpress.stackexchange.com/questions/107291/<?php the_permalink() ?>"><?php the_title(); ?></a></h3>
<?php endwhile;
else :
echo "";
endif;
?>