Basically you have to consider any Garlean that was at any point possessed by an Ascian to be a special case. We can't just assume lineage was the key, because Varis didn't have noteworthy magical acumen. My guess is that the Ascians know how to modify a Garlean so they can use magic, but kept that secret to themselves. Which explains why Zenos had some ability when he got his body back; Elidibus had made it magic-capable, that didn't go away when Zenos took it back.

Although in retrospect, I don't actually remember Zenos doing any magic after taking his body back, so I'm not exactly sure where the 'Zenos can do magic' idea came from. Zenos mostly just spent his time after taking his body back loathing the fact he was watching Fandaniel ham it up.