I think that people have widely varying natural ability in all aspects of dancing, including rhythm. But, I also think that everyone has some natural ability to hear the beat and move to it. To support my assertion, have you ever heard anyone sing "Happy Birthday" off time? E.g., you're singing "happy" while they're singing "birthday?" I've heard thousands of people sing "Happy Birthday," and I've never heard anyone sing off time. If you can move your mouth and diaphragm on time to the music, you can move your feet on time.
Further, I've noticed that many people start on time, but then drift off time. This is probably from lack of concentration and too high of a workload for their current ability. They're so consumed by following, leading, or moving their feet that they lose focus on the beat. With some more practice, often they can improve. Also, many people get off time, e.g., in swing or cha cha, because they take too big of a step on the rock step and put all their weight back on their heel; this takes too much time and when they finally rock foward, they're off time. Once their teacher points this out, they can improve dramatically.
From my own experience, when I started dancing, I had trouble hearing the beat in mambo/salsa music because this music has so much going on rhythmically that the beats are not very distinct from one another. But, with practice hearing the music, I improved dramatically.