They nailed the one feature most "new" email clients fail at... IMAP. Unfortunately your accounts are accessible to the Inky developers due to "cloud sync."
As for the cloud sync, we do so in a completely secure way. Our employees cannot access your accounts or read your mail. See http://inky.com/faq/how-does-inky-store-my-passwords-and-oth... and http://inky.com/faq for more details.