Many studies suggest using coverage concepts, such as branch coverage, as the starting point of testing, while others as the most prominent test quality indicator. Yet the relationship between coverage and fault-revelation remains unknown, yielding uncertainty and controversy. Most previous studies rely on the Clean Program Assumption, that a test suite will obtain similar coverage for both faulty and fixed ('clean') program versions. This assumption may appear intuitive, especially for bugs that denote small semantic deviations. However, we present evidence that the Clean Program Assumption does not always hold, thereby raising a critical threat to the validity of previous results. We then conducted a study using a robust experimental methodology that avoids this threat to validity, from which our primary finding is that strong mutation testing has the highest fault revelation of four widely-used criteria. Our findings also revealed that fault revelation starts to increase significantly only once relatively high levels of coverage are attained.