You mentioned that there's 'a mound that goes around the house where the garage goes.' What's its purpose? And can you be more graphic as to what/where it is? This is what I was referring to as per negative slope.
Assuming that none of this 'mound' is holding any water from draining away from the house, the 2nd contractor would be right in his thinking. Normally, a poured basement is set on gravel. And it's common to 'collect' that water and divert it somewhere on the lot, especially in your case where you're on a hilltop. There are many documented instanes where ground water is known to be pushed UP to the top of a hill, thus, from underneath your basement floor, possibly make its way into the home.
If I could pick and choose, I'd have my basement foundation sill about 12" above ground (after grading). And, I'd have a french drain installed under/around it. My best to ya and hope this helps.