But that's just it! She's a seeker and a famous hero, so the chantry cares more about her long term competence than they do about the rank and file Templars, so she doesn't have a lyrium addiction but she uses the abilities. Isn't that proof right there that the abilities are possible without...ingesting?
Basically, we don't know anything except that she's not addicted, like Eluvianix said. So presumably there's some story reason behind it. Maybe the abilities aren't the same. Maybe only some abilities require a lot of it, and others don't. We know Alistair quit and started again, so maybe you can... time it. Too many theories without more info.
But it's very... suspicious.
Coming back to Cullen, our best comparison is not so much Cassandra but Evangeline, to my mind, who definitely needed it regularly. So... I reckon Cullen will, too. I'm not too concerned on that front, altho more info is more.