What's happening is that "nativ" is used as an adverb. The DEX does not classify it as an adverb, so this might not be a correct, by-the-book thing to do, but it makes sense for such an adverb to exist; after all, English has "natively".
A lot of adjectives are used as adverbs even though the dictionary doesn't mark them as such. This comes natural because most adverbs share the form of a masculine adjective anyway (that's why it's "nativ", not "nativă"). If you want, you can always use "în mod ..." to keep things as adjectives:
Ea vorbește în mod nativ limba română. - She speaks Romanian in a native way.
But here the whole "în mod nativ" really functions as an adverb, so why not skip the extra words? Personally, I see it as a failure on the DEX's side to keep up with actual usage.
I don't know Latin, but I hope this answers your question.