Agreed, and nice saying. One can debate all day whether the old expressions of waza are still sufficient or they need to be updated with newer methods of fighting.
If you're talking about restricted fighting with rules, which is what MMA, etc., are all about, I think it's an artificial distinction, not a "newer method of fighting". Don't forget that there were sport modes of some arts back in the old days, too. Shuai Jiao (which was undoubtedly a precursor to Sumo and ju-jutsu) has had a sport/competition branch for centuries.