Straight with the sample – why does it happen…
…even if my user is a Project Administrator?
Because the single user’s permission are less important than the Team’s one – and as in this team there is a explicit deny on that permission (Edit project-level information) even if he is an Administrator he is going to get a deny.
Indeed…
That’s because you can be the CEO, but you won’t be allowed to change the delete the Team Project on your own if you’d be fired, for example :)