It's a lot more sinister than that. The very wealthy tend to donate to causes that support their own interests, motivations, or even businesses. They also donate to try and manage their public imagination as in the case of the Sackler family who knowingly manufactured the very addictive opoid that eventually came to be known as oxycotin. They became very wealthy as a result, and donated to museums, universities, and whatever else may make then seem like concerned citizens.
Or they're just brazen and don't care, like the Koch brothers. All donations from the Koch Brothers come with massive strings. You have to be behind their "less goverment is more" tea party philosophy (i.e., less regulation on their oil and coal fortune) to receive any money from them.
Good book to read if you have time:
Dark Money by Jane Mayer | PenguinRandomHouse.com: Books