Fellas, that "rumor" isn't completely right, but its not completely wrong, either. Nobody in government "mandated" the removal of zinc, but they did mandate catalytic converters on diesel engined passenger vehicles and pick-ups starting in 2008. And catalytic converters don't like zinc. So with the introduction of the diesels, the oil companies reformulated their diesel oils too.
Any oil that is rated API-SL (or CI for diesel oil) still would have enough zinc to avoid most problems...but API-SL and CI are getting mighty scarce. If the oil you are considering using is rated as API-SM it doesn't have enough zinc (840 ppm on average) if its rated CJ...it "may not" have enough zinc...it depends on whether the particular oil company "goes up to the max" of allowable zinc. If the "full 1200ppm is present, that's probably enough.