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."
IMAP is definitely a complex beast, and we're excited to offer this over many of our competitors. We believe all email users deserve a modern client with innovative features.
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.