The plugin writes the line:-
RewriteCond %{HTTP_COOKIE} !^.*(comment_author_|wordpress|wp-postpass_).*$
Also, WordPress is creating a cookie:-
Name wordpress_test_cookie
Value WP+Cookie+check
Host MY_HOST_NAME_SNIPPED_INTENTIONALLY
Path /
Secure No
Expires At End Of Session
When the user has only this cookie, because of the above line in .htaccess, the page skips the super cache and only uses the WP cache.
I am not sure generally what all other cookie names are used by wordpress in order to write the new rule, but we surely need to exclude the above mentioned cookie.