"She natively speaks Romanian."
Translation:Ea vorbește nativ limba română.
That English sentence is indeed ambiguous and clunky.
"Ea vorbește nativ limba română" means that Romanian is her native language, but in English you wouldn't phrase it like that. You would instead say something like "She is a native Romanian speaker" or "She is a native speaker of Romanian". Of course you could also say it like this in Romanian: "Ea este vorbitor nativ de limba română."
If you want to say that she speaks Romanian like a native, then that would be:
"Ea vorbește limba română ca un nativ."