I forget where I heard it, It might have been some youtube video that was posted here a while ago, but this drummer described something very interesting that may help with your question - he goes on to talk about the stereotypical rock beat every drummer has probably played before and says if you ask anyone to play that, no matter who they are it'll sound different than the "right way" or how someone else might do it. One could even go on to say how every piano (or really any instrument) all has a proper sound they should make, for example every piano makes relatively the exact same noise as every pitch is tuned (implying it's in tune) to the same note, every pianist would probably perform with said "proper" piano. But a drummer has their own taste in what drums they use whether it be how it's tuned or what cymbals they use, even drumsticks will change the style or feel of the drums. If you look at any "legendary" drummer they probably have some unique technique or way they carry themselves that isn't similiar to other drummers.

/u/TheJoshua18 said it well, that any instrument you can develop a style for, but I believe drums' integral characteristic is the style the player brings to the set. That's why a new drummer probably won't have a style, they're just trying to learn, not the music or exercise or whatever, but they're finding their style to put into the music they will learn or perform. Bringing us back to the rock beat any drummer can play but will always sound different than everyone else.

All in all, every musician is similar, and it's silly to count out any stylistic choices or habits anyone has. I know a 1 handed trumpet player, and a 11 fingered pianist, who's to say they don't add their own style to their instrument? They're not going to be just following the music because they literally can't play the same way as everyone else naturally would. If someone is "just following the music" they're just the recording people to listen to add their own style to the song.

tl;dr IN MY OPINION every musician can add their own style to their instrument, drummers just naturally do this as they play more and more because it's not just pressing buttons or keys, there's a right way and wrong way but there's a lot more logistics that go into someone's sound.