"What does the county have to do with it?
It's on private property isn't it?"

LOL. What country/planet have YOU been living on? Seriously, a "creek" is just a drainage of the land into a larger body of water (river, lake). At least here in Michigan, the Counties have "Drain Commissions" that have jurisdiction over these "drains". You can't fill them, dump into them (even just water from a driveway or sump pump), or put a crossing in them without a permit from the County Drain Commission (couple hundred dollars).

Yes, it IS private property but over the years our government at all levels (local, state, federal) has seen fit to extend control over our daily lives believing that a) they know best what's good for us and b) we may do something HARMFUL to the environment, like fill in a mud puddle that they would classify a "wetland".

The truth of the matter is that most of us who own rural property understand, appreciate and value the protection of it more than the beauracrats.