I have the same issues with W3 Total Cache: I am sure the 'system' can write to my .htaccess file because I can edit it within my WP admin through Yoast SEO plugin (I gave it 666 and could edit it after that, 664 didn't work) but W3 Total Cache still thinks it cannot access the file (and therefore a lot of things don't seem to work).
I use WinSCP (free FTP program) to find .htaccess files (Command->find files) and found out that I have .htaccess files in the following locations:
/public_html/cgi-bin/
/public_html/wp-content/cache/page_enhanced/
/public_html/wp-content/cache/tmp/
and 5 more locations, I suggest you do a search too.