I've solved my problem by giving lower "Content Hugging Priority" and "Content Compression Resistance Priority" to the image view (set everything to 250, here fullscreen) and higher - to the both labels and button (set them to 750):
(Also for the image view I've changed the mode to "Aspect Fill" and enabled "Clip Subviews") and now it works ok:
Being an iOS programming newbie, I'm sorry if my question has been too simple, but that what seems to have resolved it (moving setImageWithURL:placeholderImage:
call to viewDidAppear
did not). Also sorry for having my face 5 times at this web page - that image had the problem in the test app, so I didn't bother to search for a neutral one.