This brings me to a feeling of revulsion. I'm not sure exactly why. Maybe it's that no one can be themselves these days, like we have to absorb pieces of others to become whatever it is we see ourselves as. It seems to me like eventually it's all going to become so inbred, personality-wise, that there will be a precious few individuals.
Just to take a tangent...
What do you mean "these days"? All of the influential drummers listed on this thread would (and many have when asked) openly devulge their influences. The great classical composers all had teachers and influences. "Enter through form, then exit from it."
Could you have learned to speak locked in a small box devoid of outside language input?
Music is no different. It's an ever-evolving language. A lattice of sounds and concepts that we consciously and unconciously incorporate, imitate, and now-and-again, innovate. But I don't think we can ever seperate music from the influences of culture and media. There is nothing wrong with music being born out of our experiences, out of history. The search for a 'pure' music form, or 'pure' inspiration is futile.
John Coltrane, a voice many recognise after just a few notes (an individual?) said, "I think I was first awakened to musical exploration by Dizzy Gillespie and Bird. It was through their work that I began to learn about musical structures and the more theoretical aspects of music."
Miles Davis, an individual if there ever was one, said (about Louis Armstrong) ""You cant play nothing on modern trumpet that doesnt come from him, not even modern @$%#. I cant even remember a time when he sounded bad playing the trumpet. Never. Not even one time. He had great feeling up in his playing and he always played on the beat. I just loved the way he played and sang.""
Admit it. You listen to music.

My influences change every year. When I was young it was Gadd, Philly Joe, Max Roach, a host of Basie's drummers, and my dad (just to name the ones that first come to mind). I was also deeply influenced by countless drummers while listening to music on the radio every night before I went to sleep. I didn't always know WHO the drummer was, but I remember the licks, the ideas, the feels and would try to play them on the kit.
20 years later, I'm digging hard on Bill Stewart, Billy Martin, Stanton Moore AND all the guys I hear on the radio. I'll sit and listen to radio pop just to hear what's going on. I'll just sit, thinking about how those studio cats generate the feels and grooves they do, thinking about why they get called on again and again. Picking up a trick here and a lick there. Then I go play.
I try to pick up something from everyone I hear play, even if it is what NOT to play.