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So it is like an individual can playback sing for an individual actor - but a choir cannot. Due to the inevitable differences in frequencies and timings of members of the choir.
This gets to the heart of it. The type of person you put in an organization obviously fuels the traits of an organization but over time it will be trumped by the structure of an organization.
First off, If you haven't read "The Peter Principle" (1969) find a copy. It is funny but the humor is built on the fact that it is based on truth. Once you start getting a feel for how the normal actions of people are influenced by life inside a hierarchy then turn your head to the problem of how people get to the upper portions of the hierarchy. The leading motivations of people will be getting a raise or bonus, getting a better position or a promotion, and avoiding being terminated. The way you do this is by currying favor with people above you in the hierarchy, and creating alliances with people at the same level or below you. (And yes, "currying favor" can be as simple as simply doing a good job but it also includes making other people's work look bad...)
The number one way to accomplish this is to have a convincing, persuasive personality. The ability to actively manipulate someones impression of you is not tied to any level of morality and is commonly found in sociopaths. A famous quote, "Power corrupts ..." leads in to an observation in many financial news sources over the last 10 years that CEOs have a MUCH higher percentage of psychopaths then the general population. Just one example: Do psychopaths make good CEOs? The pretty obvious conclusion that the tendencies that lend well to the "climb to the top" also tend to lean away from moral functioning.
Existing in a framework of power is not a way to build toward actions that would be perceived as moral. A new organization can be a wonderful thing because it was created in situ. But as time passes the inexorable influences of a hierarchy will bend it in much less altruistic directions. Over time your only real influences to counter this are the need to counter outside negative perception ("Hey! They aren't moral!") and the need to fight stagnation which leads to reorganization.