Every drummer has their interpretation of time and pulse. I've played with drummers who are pushing the beat from behind, pulling the band along, or right in the pocket. Sometimes it works, sometimes it doesn't. One of my favorite drummers and best friends is super technical, still takes weekly lessons from a nationally known pro, and after 30 years playing together we still argue about where the groove should be. Occasionally I'll work with a new drummer and can 'lock up' with them right from the downbeat. Actually, I think that playing with a variety of drummers has broadened my perspective and abilities to play a variety of styles and grooves.
Here's the funniest drummer of all time, and a monster player, Dave King, digging into the rhythm section thing with Bad Plus mate Reid Anderson. Dave manages to poke fun at drummer stereotypes and impart bits of music wisdom all at the same time. Check out his "Rational Funk" series for a good laugh or two: