In the case of the American Red Cross, the turn around team that has been brought in has restored the budget while losing the soul of the organization. See this very long ProPublica article, The Corporate Takeover of the Red Cross
Rumblings about how the Red Cross has been run in recent years is nothing new. The latest article above is just one in a series where the organization has been panned.
If you went back 20 years, those Red Cross staff and volunteers would not recognize the Red Cross of today. The regionalization that has happened has gutted any local flavor from the Red Cross.
While I am sure that state and local emergency managers have seen the change, public knowledge of what has gone on and is happening today is not common knowledge.
The "brand" is still pretty good, but it is a hollow shell for what it once was in its connections within communities. Eventually there will be a disaster where the spotlight focuses on the Red Cross, like those that have shone on FEMA during a major disaster like Katrina. Probably only then will heads roll. Afterward, re-establishing a national and functional Red Cross will be no easy task.
Note that the Red Cross has stopped responding to ProPublica's requests for information and interviews. I'm sure they think the publication is on a "witch hunt" but not talking to the tribunal is like saying, "No comment."
On this last note, it used to be said that you should never get into a fight with an organization that buys ink by the barrel. Today, it is a digital knife fight and I think you are better off engaging than being silent.
Several people forwarded the article. Thanks to the Recovery Diva for being the first.