"To know Romanian"
Translation:A ști română
You're right, but it's not so strict.
"a ști" can be used for "to know someone"
"a cunoaște" can be used for "to know something"
While the first case is very natural and works just as well in virtually all situations, the second case generally sounds more awkward. And you can't use it when followed by a verb:
I know how to read. -
Eu cunosc să citesc. - wrong.
If you're unsure, just use "a ști" for knowing a fact and "a cunoaște" for knowing someone and you can't go wrong.