Most reasonably-okay to good programmers don't require much management for the project they're working on, you're right-the management needed is more often on the order of running interference to keep small, numerous, and often unconnected (to the project in question) distractions from eating away at the programmer's time.

As to complete and exact requirements, these are mythological creatures. In this case, the project management needed will be someone to enforce saying they had their chance to add that into the current requirements when it is said, "This is what you will need, right? You're absolutely sure?" and they say, "Yes," then try to come back a week or more later and say, "oh, by the way, we also need it to do...."

(Well, we can hope, can't we...?)