I'm not sure that I understand why you think it would a copyright risk. While I haven't coded mobile apps, I have coded websites professionally and it looks as though the logos are basically pulled from the e-mails themselves, perhaps from the message header and pretty much the way a favicon is pulled from a coded link in a web page header. And the author usually includes these links because they want them displayed on the client browser tabs and bookmarks.
You are mixing up two things: webpages and e-mail messages. Those are different.
"Favicon" as a feature of a webpage is a well-described standard supported by the webserver.
At least until HTML5 it didn't even have to be specified explicitly.
(However, it is an optional element: when it is absent in the file and in the default location for the server, the browser does not try to figure out where to get it from.)
E-mails do not have
any default place/format for any images. E-mail servers do not provide any images by themselves. There is no "default" location for the image.
Even if some messages include some image files, there is no reliable way to figure out which one is the logo.
So, the only way for the developer to display the logo image is to hardcode it (or a link to it, which would be an awful idea) in the app itself. And that could be a copyright violation (if there is no permission or the image is not in the public domain, and most logos aren't). It is the same way as when you cannot legally place an image taken from Amazon or Getty website to your company's website or your personal blog. Note that even Google was taken to court at some point for storing and displaying images that its search engine collected from other websites.
While Google lawyers were able to argue win this in the United States Court of Appeals for the Ninth Circuit, by arguing a "fair use":
https://en.wikipedia.org/wiki/Perfect_10,_Inc._v._Amazon.com,_Inc. , it is very clear why Kostya doesn't want to get involved.
I suspect the only way around that would be if Kostya would allow users to insert that logo themselves. (And even then they might be a risk that he can be taken to court for being complacent by not providing an adequate notice that the users might be violating copyright laws by inserting an unlicensed image.) But AFAIR (I don't see that, as I switched off all those chips), that can be done by means of the built-in "Contacts" app, where you can insert images for your correspondents on your own risk. And then that images will be shown by Aquamail.