I've spent a lot of time programming drums, listening/analyzing drums and talking to drummers over the years. Understanding their tendencies helps a lot to create realistic programming.
In this case, it is common for a drummer to hit the hat harder and open the hat to varying degrees when playing the kick and the snare. During a fill, or when the drummer moves to the ride... the hat "pedals" on quarters or eighth notes. Actually, sub consciously the drummer is always pedaling the hat... opening and closing it ever so slightly on each hit.
The hat is the timekeeper for most drummers... that is why it is continually going. It is also the item "most often on the beat" (aka, in time) while the snare actually drifts ahead and behind the beat depending on the feel. With dance music the kick is usually right on the beat, but in most other styles it drifts similar to the snare to create more feel.
There are exceptions to every rule, this is not meant to be a definitive approach - just a generalization.