Absolutely, one can be a natural at riding!
I'm really not that natural of a rider, at least equitation-wise. I often have to remind myself to sit taller, watch my heels, keep my elbows at my sides, etc. Much of that is really dependent on the conformation of the rider. I have shorter arms, so I find myself reaching forward a lot. I personally find it easier to do groundwork and training (although so much of training is made easier by working in the correct position), to convince a horse to be calm, respectful, and confident.
I agree wholly with Anebel that riding is like any other endeavor, in terms of being naturally good and having to work at it to become proficient. Some things I get easily (I can remember stupidly random facts, like the year a movie was made, or find a quote in a book I read, at the drop of a hat) and other things I can work like mad on and never really have "click" (for me personally... math in any incarnation is always a struggle).