I've had the exact situation kisamoto is talking about happen to me countless times, and I can probably count on one hand the amount of times I've won the battle over images. Sadly, the folks calling the shots on what images to use and exactly how they need to look do not care that I'm using responsive imagery to serve images to our users with appropriate file sizes, reasonable resolutions, and ensure crops have editor selected focal points.
When I say these folks get upset over slight pixelization, I'm not even talking about pixelization where everyone can tell it's a low quality image. I'm talking about situations where people are upset they can't read an iPhone screen someone is holding in the background when they are viewing it on their 4K display (note: that particular phone isn't the focal point of the shot, nor does it have anything to add to it; it's just someone staged back there to make the shot feel more alive, mind you!).
It's disheartening because I do want to deliver the best experience possible and try to do everything in my power to accomplish it, but sometimes I lose out and folks force their megabyte imagery.