The Dealer wont check the oil for any reason unless they are doing a point check or change, the muffler pipe wont warrant checking oil cap.
The deal also wont pay for cleaning out the motor unless there is a Tech Bulletin or a Recall, you would want to look up your model and research the Recalls on it.
Black Sludge is indicative of burnt oil or too much carbon build-up, they would immediately blame this on not doing regular oil changes at 3k mile intervals.
To prevent this from happening and actually will clean out motor is to use Full Synthetic oil from now on.
Good Luck
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