While it is certainly distasteful when someone takes credit for something that they had no involvement in, I would argue that it's also possible to too far in the other direction. All too many programmers (myself included!) won't take credit for anything unless they did 100% of the work. Well, as I'm slowly learning, it is possible to be nuanced. It is possible to take partial credit and to understand that saying that you led an effort doesn't automatically mean that you did 100% of the work.

Part of being a leader is convincing other people to listen to you. A very good way of doing that is to be able to point to publicly recorded instances where you've taken leadership in the past and delivered good results. If you don't take credit as a leader, you'll very soon find yourself displaced (for better or worse) by someone who does.

Yes and no. Let's say your team has pulled off a major coup. As a (good) manager you very publicly say that all the credit belongs to the team. The team are happy and they love you. But the power players understand your real message.