Kostya,
The question about messages getting marked "read" when people access account with multiple devices, where at least one uses pop3, is very frequent. (You have one pending in the Russian part now as well.)
(Unless I missed it somehow,) I discovered that neither English nor Russian FAQ has that information.
There is this item:
Why are messages loaded using POP3 not marked as read on the server?
POP3 has no support for marking messages as read or unread. Some mail services mark messages as read once they’ve been downloaded by a mail application, some do not.
But it doesn't discuss the corollary of that. And it is not that obvious step for many app users.
So, you probably want to consider adding an item to the FAQ about this.