The word style is the operative one here. I've heard this discussion a few times before within my drumming crowd & it's always the same two sides: "Not playing the song note for note is disrespectful to the original drummer. They spent a lot of time getting that right only for you to mess it up".I wonder if I am missing out on some joy by not working on original music more. My only competition would be myself so there's some relief in that but more importantly, my own style would develop if I worked on originals. Right now that isn't really happening.
"Play it as close to the original as you can, but put your own flavor into it. Trust me, the original drummer was just doing the same & that's how it came out on tape".
I currently play covers in a blues band & I assure you the latter is the way to go. You don't want to stifle your skills by just going through the motions of another player. The audience won't know (or care) as much as you think they do.
Now...that being said, if you decided to "go all Neil Peart" during a Johnny Cash song, they might have issue, but I doubt you're like that.