Casual users don't care about the app "looking wrong". They do care about the app not working like other apps on their phone, though.
If you can't copy or paste things, or if the navigation is backwards, or if the calendar looks weird etc etc - it all causes some minor frustrations, when things don't behave as user wants them to behave.
They don't know what "native" means, obviously - they don't have that knowledge. They just know crappy apps from well-behaving apps, because they have a frame of reference (vendor-supplied native apps).
Perhaps they're not complaining because they've just accepted that it probably doesn't work and so don't even try anymore.
My SO has stopped trying to copy/pasting stuff, I now always just get screenshots, both from mobile and her PC.
At work, almost none of the customers I interact with copy/paste stuff, they send screenshots as well. Like, "can you send me the order number?" will result in a screenshot of the order number control, or often just the whole order window.
Granted this is my personal experience, I can't say this is the case for every single user out there.