It's more the fact that they don't want to acknowledge it publicly, and pretend there isn't a problem, or the problem isn't as bad as everyone makes it out to be that's the issue.
They make their own case for being talked about poorly because the vast, vast majority of them are unwilling to take any criticism that will make them look bad because their feelings got hurt.
Nobody says the system isn't broken, because no fucking shit, that's obvious. The problem is that the rich do little to give a fuck the system is broken because they continue to take advantage of it because people are unwilling to call them out on it, as they're the ones paying the politicians to not say anything about, and in many cases, are willing to become those politicians to start pulling the strings to make sure the system stays broken.
While I'm not sure exactly what you had hoped for in a discussion of this topic with the way you framed the op, but I feel you are way, way off in what you're trying to imply in regards to the public image of the rich as if they're not doing anything themselves to make the problem worse.
One of them recently was so pouty people were mean to them, he decided to run for President, and then gave no actual answers at a town hall meeting to explain any of his positions.
I kinda feel more 70-30 on "hate the game not the player".
You DO get people who use their wealth for good...shame how few and far between they are.
I'd say it's about 1% of the 99% that gives a fuck.