I mean that’s true of the english term as well. But if someone says they can’t cook i default to thinking they order out every meal or use a microwave fot cup of ramen. Making sandwiches, salads, and other cold foods is still a skill but there’s no word such as cold-cutlerist and i refuse andwich artist.
I think that’s grammatically true but i tend to think of it more in terms of colloquialisms or slang. I imagine intransitive use of the verb developed out of convenience for lack of a lazy alternative. “I can’t prepare food” would either suggest you require assistance to eat, you can’t legally work at a restaurant, or your aristocratic status is beyond that of a mere peasant who has seen a kitchen before.