Every iOS email app that has push notifications stores you credentials (username+password) on the app providers SERVER and has FULL access to all your emails.
That's a fact.
That's actually not true. There are several ways to implement push email on iOS that do not require storing credentials on the server side:
- Some email providers can send Apple push notifications to the stock Mail app; that obviously includes iCloud email, but also Fastmail and Mailbox.org.
- Some email providers offer their own email apps, and can of course implement push notifications for those. That includes Fastmail, Protonmail, Tutanota and probably others.
- You can use Exchange Activesync (which has its own efficient push mechanism) with the stock Mail app. This is supported by Outlook.com and Google business accounts.
These are all safe methods.
Generally, when choosing an email client, it is safest to pick the stock Apple client, an open source client like Thunderbird, or, if available, the email provider's own app.
But yes, this incident illustrates nicely why storing account credentials on 3rd party servers is a bad idea.