Metallica is the prime example.
Lars Ulrich played some charmingly-quirky beats in his career, but without the supreme songwriting of the rest of the band he would have ended up forgotten. When you see him live it's obvious he can't really hold anything more than a simple beat. Actually, I think a lot of riffs from the early thrash days sound so broken not because of some advanced rhythmic abilities, but because lars came up with weird drum lines that didn't quite resolve to 4/4, without realizing it. It's still a debate to this day what exact time signature is used in the song Master of Puppets (hint: is involves booze).