Anything can be taught. Some people have more natural ability than others.
I like this. It makes sense to me: It's simple and direct, and reflects what we know about physiology and learning.
I have a hard time with arguments about being born with or not born with some ability and that marking you for life. This is especially true when it comes to highly skilled issues. I absolutely think that a sense of rhythm can be taught but some people are going to have an easier time of it, whether due to the way their brain is wired, their past experience, the innervation of their fine control muscles, etc.
Consider an example from another field: distance running. You go to a local 5k and watch as people stream past the finish line. Up front you've got lithe, gazelle-like athletes who whiz by seemingly without effort. At the back come relatively chunky folks, comparatively clumsy with movement, pounding their way home with obvious effort. Knowing people across this spectrum (and happy that every one of them is out there, from fastest to slowest) I would bet dollars to dimes that the people up front are far, far better trained than the people at the back. Their weekly mileage will be much higher, their workouts more challenging and extreme.
BUT this is not to say that if we picked up someone from the back and trained them for a few years that they would be running in the lead. To be in the lead, you have to have certain physiological traits, for example a large heart stroke volume or a greater number of slow twitch muscle fibers than fast twitch muscle fibers (this is why you never seen champion sprinters turn into top marathoners and vice versa - wrong muscle fiber percentages). Some of these factors can be improved with training (stroke volume) some can't.
Second BUT, what we
can say is that the newly trained person will definitely be
better than they were. Maybe they won't be the fastest runner out there but they may be well toward the front instead of bringing up the rear. And given their physiological make-up, it may take them several years to get to a point that a better endowed athlete might get to in one year, but they'll get there.
I firmly believe that the vast majority of us do not operate any where near our maximum potential in almost every area. We simply do not have the time, resources or desire to do so. The true greats among us, whether they're drummers or marathoners, artists or research scientists, are the ones who had the interest, and the personal and external resources to follow a path with complete focus.