As far as I can tell, the bug appears to be that iOS just completely ignores the fetch settings and always uses automatic mode which only automatically downloads mail when the phone is charging and on Wi-Fi.
fwiw, I have two email "accounts" configured on my phone. Because I very rarely use email on my phone, both accounts are set to manual fetch and push is off. Nevertheless, whenever I charge the phone, it will download email. In other words, it is completely ignoring the account settings when on charge.
Also, because I did use phone email yesterday, I discovered some of the issues noted in this thread: reappearance of deleted emails, and not picking up new emails. Email on my mac was behaving as expected. (Because one of the accounts mentioned above is my own email server, I could see that the deleted emails were not present on the server.)