You're confusing the issue. This isn't about SSH versus FTP: it's about whether or not the Apache user running your website can also write to the filesystem inside of your document root. The Wordpress update feature is actually able to use FTP as the means of updating the site.
That's true; I was oversimplifying the issue. Most shared hosting web hosts run PHP files with the same user that you FTP with. If WP can't update itself in these cases then the user cannot write files via FTP. If a user connects via SSH then chances are they are comfortable changing directory permissions to do an update.
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You're confusing the issue. This isn't about SSH versus FTP: it's about whether or not the Apache user running your website can also write to the filesystem inside of your document root. The Wordpress update feature is actually able to use FTP as the means of updating the site.
That's true; I was oversimplifying the issue. Most shared hosting web hosts run PHP files with the same user that you FTP with. If WP can't update itself in these cases then the user cannot write files via FTP. If a user connects via SSH then chances are they are comfortable changing directory permissions to do an update.