OP is right though, that all CreditTaker's peers know he isn't doing any of the work, but it doesn't matter because companies are hierarchal and CreditTaker is the only one talking to execs above him, so his story is what gets passed around as reality. His peers who know the truth are too busy doing the actual work.
Taking credit doesn't look just one way. Very few mid-level management types will delegate work then when the work is completed they go to their direct report and say "Hey look what I created all by myself with no help. Pretty great huh!?" What happens more commonly is that they will delegate a project to team members A & B and have them come up with a solution to a problem. When the project is complete A & B show it to manager I. Manager I then goes to manager II and says "Here is what my team came up with as a solution to our current problem." Manager I had little to no involvement in the work or development of the solution, but they present it as though they had. That happens constantly in the working world. A good manager and leader will always mention, by name, who did the work.
It's credit-taking all the way up.