In my experience and observation over 45+ years of drumming, I believe that a person's DNA has much to do with their potential ability/skill level. Drumming is a rather physical (even athletic in some cases) activity, and like any physical/athletic activity, there are certain factors that contribute to an individual's performance ceiling. Bone structure certainly plays a role, as do muscles and nerves. The rate at which the brain fires and sends signals to the limbs is also not necessarily equal. There are what is known as "fast twitch" and "slow twitch" muscle fibers, and these develop differently among different people. The fast twitch type tend to control the "sprinting" activities, whereas the slow twitch would affect the endurance more. Some drummers are very fast for short bursts, but not necessarily for long stretches. Others can keep a particular pattern going indefinitely, or play 4+ hour gigs every night. Also, different players require different amounts of practice to maintain peak performance. There will always those players, who, regardless of how much time they put in, are never able to play what certain others can, whether it be speed, four-way independence, complex odd time signatures, or even basic feel. People are simply different. The word we use to describe this difference is talent. Different people have different levels of raw talent. I'm sure everybody reading this is aware that Buddy Rich is quite often considered the best drummer of all time (particulars of style not withstanding). I'm also sure most would agree that, regardless of how much time they spent practicing, they don't believe they'll ever be able to play like Buddy (present company included). And why not? Because no one else is Buddy Rich! (has his DNA).
If you look at any professional sport, there are those who excel more in certain aspects of their game, and much of this can be attributed to their basic body size, weight, type, etc. In American Football, for example, the defensive linemen practice the same number of hours per day/week/month as the running backs and wide receivers, but could never run the 40 yard dash in the same time. Likewise, those zippy ball carriers probably can't lift as much dead weight in the gym as the guys on the line. A simple look at their body types will show you why.
So, with drumming, the length of hands, fingers, arms, legs, etc., and the makeup of muscle fibers, combined with brain and nerve activity (in short, a person's DNA), can certainly have an impact, IMO.